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Call number: | 9783319508535:ONLINE Show nearby items on shelf |
Title: | Algebra II Textbook for Students of Mathematics |
Author(s): |
Alexey L Gorodentsev |
Date: | 2017 |
Size: | 1 online resource (XV, 370 p. 155 illus., 2 illus. in color p.) |
Contents: | §1Tensor Products -- §2 Tensor Algebras -- §3 Symmetric Functions -- §4 Calculus of Arrays, Tableaux, and Diagrams -- §5 Basic Notions of Representation Theory -- §6 Representations of Finite Groups in Greater Detail -- §7 |
Representations of Symmetric Groups -- §8 sl_2-Modules -- §9 Categories and Functors -- §10 Extensions of Commutative Rings -- §11 Affine Algebraic Geometry -- §12 Algebraic Manifolds -- §13 Algebraic Field Extensions -- §14 Examples | |
of Galois Groups -- References -- Hints to Some Exercises -- Index | |
ISBN: | 9783319508535 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebra , Mathematics , Algebra |
Availability: | Click
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Call number: | 9783319475127:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators: Groups, Geometry and Applications |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (VIII, 239 p. 23 illus., 11 illus. in color p.) |
Contents: | Pseudo-Differential Operators on the Affine Group -- Pseudo-Differential Operators on Non-Isotropic Heisenberg Groups with Multi-Dimensional Center -- Curvatures of the Heisenberg Group -- Ellipticity with Global Projection Conditions |
-- Multilinear Localization Operators Associated to Quaternion Fourier Transforms -- A Time-Frequency Relationship between the Langevin Equation and the Harmonic Oscillator -- Are There Quantum Operators and Wave Functions in Standard | |
Probability Theory -- A Class of Non-Markovian Pseudo-Differential Operators of Lévy Type -- On the Solvability of Some Systems of Integro-Differential Equations with Anomalous Diffusion -- Visualizing Discrete Complex-Valued | |
Time-Frequency Representations -- The Reassigned Spectrogram of the Stockwell transform -- Continuous Multi-Wavelet Transforms for Blind Signal Separation. | |
ISBN: | 9783319475127 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Operator theory , Partial differential equations , Information theory , Differential geometry , Probabilities , Mathematics , Operator Theory , Partial Differential Equations , Differential Geometry , Probability Theory and Stochastic Processes , Information and Communication, Circuits |
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Call number: | SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf |
Title: | Quantization on Nilpotent Lie Groups |
Author(s): |
Veronique Fischer |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (557 p.) |
Note: | 10.1007/978-3-319-29558-9 |
Contents: | Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index |
ISBN: | 9783319295589 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics: 314 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics |
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Call number: | SPRINGER-2014-9789462390249:ONLINE Show nearby items on shelf |
Title: | Recent Progress in General Topology III [electronic resource] |
Author(s): |
K.P Hart J van Mill P Simon |
Date: | 2014 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland,1992 and 2002). The boo k was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in2002. The following areas experienced signifi cant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems |
Contents: | Topological Homogeneity |
Some Recent Progress Concerning Topology of Fractals | |
A biased view of topology as a tool in functional analysis | |
Large scale versus small scale | |
Descriptive aspects of Rosenthal compacta | |
Minimality conditions in topological groups | |
Set | |
Theoretic update on Topology | |
Topics in Dimension Theory | |
Representations of dynamical systems on Banach spaces | |
Generalized metrizable spaces | |
Permanence in Coarse Geometry | |
Selections and Hyperspaces | |
Continuum Theory | |
Almost disjoint families and topology | |
Some Topics in Geometric Topology II | |
Topologic | |
ISBN: | 9789462390249 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Logic, Symbolic and mathematical , Topology |
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Call number: | SPRINGER-2014-9783319079684:ONLINE Show nearby items on shelf |
Title: | Representation Theory [electronic resource] : A Homological Algebra Point of View |
Author(s): |
Alexander Zimmermann |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra andrepresentations of groups to block the ory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more generalalgebras, such as symmetric finite dimensional algebras over a fie ld. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their maininvariants and links between them. Group theoretical applications of these theories are given such as the structure of blocks of cyclic defect groups whenever appropriate. Overall, many methods from the representation theory ofalgebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups andalgebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use |
Contents: | Rings, Algebras and Modules |
Modular Representations of Finite Groups | |
Abelian and Triangulated Categories | |
Morita theory | |
Stable Module Categories | |
Derived Equivalences | |
ISBN: | 9783319079684 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Algebra and Applications, 1572-5553 : v19 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf |
Title: | Probability on Compact Lie Groups [electronic resource] |
Author(s): |
David Applebaum |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects |
Contents: | Introduction |
1.Lie Groups | |
2.Representations, Peter | |
Weyl Theory and Weights | |
3.Analysis on Compact Lie Groups | |
4.Probability Measures on Compact Lie Groups | |
5.Convolution Semigroups of Measures | |
6.Deconvolution Density Estimation | |
Appendices | |
Index | |
Bibliography | |
ISBN: | 9783319078427 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability Theory and Stochastic Modelling, 2199-3130 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319057927:ONLINE Show nearby items on shelf |
Title: | Principles of Harmonic Analysis [electronic resource] |
Author(s): |
Anton Deitmar Siegfried Echterhoff |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respectivegeneralizations to non-abelian grou ps, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelicgroups, as well as a complementary section on direct an d projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonicanalysis and for researchers seeking to apply it |
Contents: | 1. Haar Integration |
2. Banach Algebras | |
3. Duality for Abelian Groups | |
4. The Structure of LCA | |
Groups | |
5. Operators on Hilbert Spaces | |
6. Representations | |
7. Compact Groups | |
8. Direct Integrals | |
9. The Selberg Trace Formula | |
10. The Heisenberg Group | |
11. SL2(R) | |
12. Wavelets | |
13. p | |
adic numbers and adeles | |
A. Topology | |
B. Measure and Integration | |
C: Functional Analysis | |
ISBN: | 9783319057927 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Harmonic analysis , Visualization |
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Call number: | SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf |
Title: | Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource] |
Author(s): |
Mahir Can Zhenheng Li Benjamin Steinberg Qiang Wang |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids |
Contents: | On Algebraic Semi groups and Monoids (M. Brion) |
Algebraic Semi groups are Strongly | |
regular (M. Brion, L. E. Renner) | |
Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha) | |
Representations of Reductive Normal Algebraic Monoids (S. Doty) | |
On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma) | |
The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang) | |
Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao) | |
Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen) | |
The Endomorphisms Monoid of a | |
ISBN: | 9781493909384 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Fields Institute Communications, 1069-5265 : v71 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics |
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Call number: | SPRINGER-2014-9781461485353:ONLINE Show nearby items on shelf |
Title: | Coherent States, Wavelets, and Their Generalizations [electronic resource] |
Author(s): |
Syed Twareque Ali Jean-Pierre Antoine Jean-Pierre Gazeau |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) andvarious generalizations o f wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherentstates, wavelets, and some of their generaliz ations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take aclassical-like view of quantum states in physics. Starting from the standar d theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are squareintegrable over a homogeneous space a further step allows one to dispense with the group context altog ether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensionalwavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups,Gazeau-Klauder coherent states,coherent states forthe relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potentialapplications, from the quantum physicallyoriented,likethe quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research forgraduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research liter |
Contents: | Canonical Coherent States |
Positive Operator | |
Valued Measures and Frames | |
Some Group Theory | |
Hilbert Spaces | |
Square Integrable and Holomorphic Kernels | |
Covariant Coherent States | |
Coherent States from Square Integrable Representations | |
Some Examples and Generalizations | |
CS of General Semidirect Product Groups | |
CS of Product Groups | |
CS Quantizations and Probabilistic Aspects | |
Direct Wavelet Transforms | |
Multidimensional Wavelets | |
Wavelets Related to Other G Groups | |
The Discretization Problem | |
Frames Sampling and All That | |
ISBN: | 9781461485353 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Group theory , Quantum theory |
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Call number: | SPRINGER-2013-9784431542704:ONLINE Show nearby items on shelf |
Title: | Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop |
Author(s): |
Vladimir Dobrev |
Date: | 2013 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to asystem yields in general so me notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantumgroups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples ofthese new trends are presented in this volume, based on contributions fr om the Workshop Lie Theory and Its Applications in Physics held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience ofmathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theo ry |
Note: | Springer eBooks |
ISBN: | 9784431542704 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v36 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Geometry |
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Call number: | SPRINGER-2013-9783642394850:ONLINE Show nearby items on shelf |
Title: | Algebras, Quivers and Representations [electronic resource] : The Abel Symposium 2011 |
Author(s): |
Aslak Bakke Buan Idun Reiten yvind Solberg |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas ofmathematics like commutati ve algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systemsand triangulated categories. In addition, it in cludes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students inalgebra, representation theory and triangulated categories |
Note: | Springer eBooks |
Contents: | C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions |
L. Avramov: (Contravariant) Koszul duality for DG algebras | |
R. Buchweitz: The fundamental group of a morphism in a triangulated category | |
K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras | |
D. Happel: Algebras of finite global dimension | |
K. Igusa (with G. Todorov): Continuous Frobenius categories | |
D.A. Jorgensen: Triangle functors from generic hypersurfaces | |
Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian | |
H. Krause: Mo | |
ISBN: | 9783642394850 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia, 2193-2808 : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf |
Title: | Lie Groups [electronic resource] |
Author(s): |
Daniel Bump |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations |
Note: | Springer eBooks |
Contents: | Part I: Compact Topological Groups |
1 Haar Measure | |
2 Schur Orthogonality | |
3 Compact Operators | |
4 The PeterWeyl Theorem | |
Part II: Compact Lie Groups | |
5 Lie Subgroups of GL(n,C) | |
6 Vector Fields | |
7 Left | |
Invariant Vector Fields | |
8 The Exponential Map | |
9 Tensors and Universal Properties | |
10 The Universal Enveloping Algebra | |
11 Extension of Scalars | |
12 Representations of sl(2,C) | |
13 The Universal Cover | |
14 The Local Frobenius Theorem | |
15 Tori | |
16 Geodesics and Maximal Tori | |
17 The Weyl Integration Formula | |
18 The Root System | |
19 Examples of Root Systems | |
ISBN: | 9781461480242 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v225 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups |
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Call number: | SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf |
Title: | Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday |
Author(s): |
Alan Huckleberry Ivan Penkov Gregg Zuckerman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted |
Note: | Springer eBooks |
Contents: | Preface |
Real group orbits on flag manifolds | |
Complex connections with trivial holonomy | |
Indefinite harmonic theory and harmonic spinors | |
Twistor theory and the harmonic hull | |
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets | |
Propagation of the multiplicity | |
freeness property for holomorphic vector bundles | |
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains | |
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf | |
Weakly harmonic Maa forms and the princi | |
ISBN: | 9781461471936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v306 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf |
Title: | Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program |
Author(s): |
Monika Ludwig Vitali D Milman Vladimir Pestov Nicole Tomczak-Jaegermann |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
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Note: | Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science |
Note: | Springer eBooks |
Contents: | Preface |
The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero) | |
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova) | |
On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain) | |
Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow) | |
On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman) | |
Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili) | |
F | |
ISBN: | 9781461464068 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fields Institute Communications, 1069-5265 : v68 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9781461463337:ONLINE Show nearby items on shelf |
Title: | The Mathematics of Frobenius in Context [electronic resource] A Journey Through 18th to 20th Century Mathematics |
Author(s): |
Thomas Hawkins |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Frobenius is best known as creator of the theory of group characters and representations, but his name is attached to a multitude of theorems and concepts from a broad spectrum of mathematical disciplines. In this book hismathematicsis presented in c ontext in two senses. The first provides the reader with the historical background necessary to understand why Frobenius undertook to solve a particular problem and to appreciate the magnitude of hisachievement. Part of the context involves Frobenius trai ning in the Berlin school of mathematics presided over by Weierstrass, Kronecker, and Kummer, from whom he learned disciplinary ideals as well as theorems. Frobeniusmathematics is also presented in context in that the author traces the ways in which his w ork was subsequently applied, developed, and ultimately incorporated into present-day mathematics. As a consequence of the contextualapproach, the reader will encounter a broad swath of diverse and important strands of 18th20th century mathematics, rangin g from the work of Lagrange and Laplace on stability of linear systems of differential equations to the theoryof complex abelian varieties. The book is divided into three parts. Part I provides an overview of Frobenius entire mathematical career and thus serves as an introduction to the main body of the book. Here, within the framework ofhis educational and professional career, his contributions to mathematics and the attendant backgrounds are briefly sketched and their subsequent impact upon the developm ent of mathematics indicated. Part II presents the development ofcore aspects of linear algebra up to and including the work of Weierstrass and Kronecker. The chapters of Part III deal in depth with Frobenius major works and can be read independently of o ne another. Thomas Hawkins was awarded theMAA Chauvenet Prize for expository writing and was the first recipient of the AMS Whiteman Prize for historical exposition. His las |
Note: | Springer eBooks |
Contents: | 1. A Berlin Education |
2. Professor at the Zurich Polytechnic | |
3. Berlin Professor | |
4. The Paradigm | |
5. Further Development of the Paradigm | |
6. The Problem of Pfaff | |
7. The Cayley | |
Hermite Problem and Matrix Algebra | |
8. Arithmetical Investigations: Linear Algebra | |
9. Arithmetical Investigations: Groups | |
10. Abelian Functions | |
11. Frobenius' Generalized Theory of Theta Functions | |
12. The Group Determinant Problem | |
13. Group Characters and Representations | |
14. Alternate Routes to Representation Theory | |
15. Characters and Representations after 1897 | |
16. Loose Ends | |
ISBN: | 9781461463337 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Sources and Studies in the History of Mathematics and Physical Sciences, 2196-8810 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory |
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Call number: | SPRINGER-2013-9781461458883:ONLINE Show nearby items on shelf |
Title: | Drinfeld Moduli Schemes and Automorphic Forms [electronic resource] : The Theory of Elliptic Modules with Applications |
Author(s): |
Yuval Z Flicker |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the authors original work establishing the correspondence between ell-adic rank r Galois representations andautomorphic representations of GL( r) over a function field, in the local case, and,in the global case, under a restriction at a single place. It develops Drinfelds theory of elliptic modules, their moduli schemes and coveringschemes, the simple trace formula, the fixed point formula, as w ell as the congruence relations and a simpleconverse theorem, not yet published anywhere. This version, based on a recent course taught by the author at TheOhioState University, is updated with references to research that has extended and developed the or iginal work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as avaluable resource to facilitate anentrance to this fascinating area of mathematics |
Note: | Springer eBooks |
Contents: | Elliptic Moduli |
Hecke Correspondences | |
Trace Formulae | |
Higher Recipropcity Laws. | |
ISBN: | 9781461458883 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Number theory |
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Call number: | SPRINGER-2013-9781461454502:ONLINE Show nearby items on shelf |
Title: | Lectures on Finitely Generated Solvable Groups [electronic resource] |
Author(s): |
Katalin A Bencsath Marianna C Bonanome Margaret H Dean Marcos Zyman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lectures on Finitely Generated Solvable Groups are based on the Topics in Group Theory course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Centerof the City University of Ne w York. While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them. The study of finitely generatedsolvable groups involves many different threads thereforethe se notes contain discussions on HNN extensions amalgamated and wreath products and other concepts from combinatorial group theory as well as commutative algebra. Alongwith Baumslags Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvablegroups. Examples are also supplied, which help illuminate many of the key concepts contained in the notes. Requiring onl y a modest initial group theory background from graduate and post-graduate students, these notes provide afield guide to the class of finitely generated solvable groups froma combinatorial group theory perspective |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Preliminaries | |
Tools: Presentations and their Calculus | |
Constructions | |
Representations andaTheorem of Krasner and Kaloujnine | |
The Bieri | |
Strebel Theorems | |
Finitely Generated Metabelian Groups | |
An Embedding Theorem for Finitely Generated Metabelian Groups | |
Sketch of Proof of Lemma 1.1 | |
Theorem 2.1 Details | |
Presenting an (Internal) HNN | |
Extension | |
References | |
ISBN: | 9781461454502 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Combinatorics |
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Call number: | SPRINGER-2013-9781447148326:ONLINE Show nearby items on shelf |
Title: | Modular Representation Theory of Finite Groups [electronic resource] |
Author(s): |
Peter Schneider |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
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Note: | Springer 2013 e-book collections |
Note: | Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for exampleover the fieldof complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finitegroups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as wellas Green's direct analysis of indecomposable representations. Ther e is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's workthen establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple acategory a block is by the size and structure of its so-called 'defect group'. All these concepts are made explic it for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentationis strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the read er the group theoretic approach. In particular, in the case of defect groups a detailed proof of theequivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with thesemisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwis |
Note: | Springer eBooks |
Contents: | Prerequisites in module theory |
The Cartan{Brauer triangle | |
The Brauer character | |
Green's theory of indecomposable modules | |
Blocks | |
ISBN: | 9781447148326 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Title: | New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number |
Author(s): |
Garret Sobczyk |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
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Note: | The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s |
Note: | Springer eBooks |
Contents: | 1 Modular Number Systems |
2 Complex and Hyperbolic Numbers | |
3 Geometric Algebra | |
4 Vector Spaces and Matrices | |
5 Outer Product and Determinants | |
6 Systems of Linear Equations | |
7 Linear Transformations on R^n | |
8 Structure of a Linear Operator | |
9 Linear and Bilinear Forms | |
10 Hermitian Inner Product Spaces | |
11 Geometry of Moving Planes | |
12 Representations of the Symmetric Group | |
13 Calculus on m | |
Surfaces | |
14 Differential Geometry of Curves | |
15 Differential Geometry of k | |
Surfaces | |
16 Mappings Between Surfaces | |
17 Non | |
Euclidean and Projective Geometries | |
18 Lie Gr | |
ISBN: | 9780817683856 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics |
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Title: | Groups [electronic resource] : An Introduction to Ideas and Methods of the Theory of Groups |
Author(s): |
Antonio Mach |
Date: | 2012 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
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Note: | Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hlders program for attacking thisproblem in the case of finite gro ups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied bothin the finite and infinite case. Permutation groups and are treated in detail their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and thecohomology theory of groups the latter with special emphasis on the extension proble m. The sections are followed by exercises hints to the solution are given, and for most of them a complete solution is provided |
Note: | Springer eBooks |
Contents: | Normal Subgroups, Conjugation and Isomorphism Theorems |
Group Actions and Permutation Groups | |
Generators and Relations | |
Nilpotent Groups and Solvable Groups | |
Representations | |
Extensions and Cohomology | |
Solution to the exercises | |
ISBN: | 9788847024212 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | UNITEXT, 2038-5714 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9783642308055:ONLINE Show nearby items on shelf |
Title: | An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists [electronic resource] |
Author(s): |
Hajime Ishimori Tatsuo Kobayashi Hiroshi Ohki Hiroshi Okada Yusuke Shimizu Morimitsu Tanimoto |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
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Note: | These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics.While Abelian discrete sym metries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand thethree-generation flavor structure in particular. Ind eed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark andlepton masses, and mixing angles by assuming non-Abelian discrete flavor symmet ries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abeliandiscrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory - e.g. the string theory or compactification via orbifolding thereby providing a possible bridge between the underlying theoryand the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical a spects of many concrete groups and shows how to derive conjugacy classes, characters, representations,and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest |
Note: | Springer eBooks |
Contents: | Introduction |
Basics of Finite Groups | |
Subgroups and Decompositions of Multiplets | |
Anomalies | |
Non | |
Abelian Discrete Symmetry in Quark/Lepton Flavor Models | |
Useful Theorems | |
Representations of S4 in Different Bases | |
Representations of A4 in Different Bases | |
Representations of A5 in Different Bases | |
Representations of T1 in Different Bases | |
Other Smaller Groups | |
References | |
ISBN: | 9783642308055 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v858 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Group theory , Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2012-9783642227172:ONLINE Show nearby items on shelf |
Title: | The Schrdinger-Virasoro Algebra [electronic resource] Mathematical structure and dynamical Schrdinger symmetries |
Author(s): |
Jrmie Unterberger Claude Roger |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schrdinger-Virasoro algebra. Just as Poincar invariance or conformal (Virasoro) invarianceplay a key role in understanding , respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study ofsome models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Liealgebra touches upon topics as various as statistical physics, vertex algebras, Po isson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and thespectral theory of Schrdinger operators. |
Note: | Springer eBooks |
Contents: | Introduction |
Geometric Definitions of SV | |
Basic Algebraic and Geometric Features | |
Coadjoint Representaion | |
Induced Representations and Verma Modules | |
Coinduced Representations | |
Vertex Representations | |
Cohomology, Extensions and Deformations | |
Action of sv on Schrdinger and Dirac Operators | |
Monodromy of Schrdinger Operators | |
Poisson Structures and Schrdinger Operators | |
Supersymmetric Extensions of sv | |
Appendix to chapter 6 | |
Appendix to chapter 11 | |
Index | |
ISBN: | 9783642227172 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Algebra , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2012-9783642154829:ONLINE Show nearby items on shelf |
Title: | Symmetries and Group Theory in Particle Physics [electronic resource] : An Introduction to Space-Time and Internal Symmetries |
Author(s): |
Giovanni Costa Gianluigi Fogli |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is anintroduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of theMinkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standardmodel of particle physics. This book, based on several courses given by th e authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge ofclassical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures |
Note: | Springer eBooks |
Contents: | Introduction to Lie Groups and their Representations |
The Rotation Group | |
The Homogeneous Lorentz Group | |
The Poincare Transformation | |
One Particle and Two Particle States | |
Discrete Operations | |
Relativistic Equations | |
Unitary Symmetries | |
Gauge Symmetries | |
Rotation Matrices and Clebsch | |
Gordan Coeficients | |
Symmetric Goups and Identical Particles | |
Young Tableaux and Irreducible Representations ot he Unitary Groups | |
Solutions | |
Index | |
ISBN: | 9783642154829 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v823 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2012-9783034802604:ONLINE Show nearby items on shelf |
Title: | Representations of Finite Groups: Local Cohomology and Support [electronic resource] |
Author(s): |
David J Benson Srikanth Iyengar Henning Krause |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas fromcommutative algebra, co homology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been DanielQuillens description of the algebraic variety co rresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods ofalgebraic geometry to obtain representation theoretic information. Thei r work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutativeHopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins classification ofthick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localiz ing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approachto address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with rin g of operators. The book serves as an introduction to this circle of ideas |
Note: | Springer eBooks |
Contents: | Preface |
1 Monday | |
1.1 Overview | |
1.2 Modules over group algebras | |
1.3 Triangulated categories | |
1.4 Exercises | |
2 Tuesday | |
2.1 Perfect complexes over commutative rings | |
2.2 Brown representability and localization | |
2.3 The stable module category of a finite group | |
2.4 Exercises | |
3 Wednesday | |
3.1 | |
3.2 Koszul objects and support | |
3.3 The homotopy category of injectives | |
3.4 Exercises | |
4 Thursday | |
4.1 Stratifying triangulated categories | |
4.2 Consequences of stratification | |
4.3 The Klein four group | |
4.4 Exercises | |
5 Friday | |
5.1 Localising subcategories of D | |
ISBN: | 9783034802604 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Oberwolfach Seminars : v43 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9781461419396:ONLINE Show nearby items on shelf |
Title: | Spectra of Graphs [electronic resource] |
Author(s): |
Andries E Brouwer Willem H Haemers |
Date: | 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromaticnumber and Shannon capac ity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of some new material on trees, strongly regular graphs, two-graphs, association schemes,p-ranks of configurations and similar topics. Exerc ises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, referencesat the end of the book, an author and subject index enrich the text. Spect ra of Graphs is written for researchers, teachers and students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra andeigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theo rem and eigenvalue interlacing are included |
Note: | Springer eBooks |
Contents: | Graph spectrum |
Linear algebra | |
Eigenvalues and eigenvectors of graphs | |
The second largest eigenvalue | |
Trees | |
Groups and graphs | |
Topology | |
Euclidean representations | |
Strongly regular graphs | |
Regular two | |
graphs | |
Association schemes | |
Distance regular graphs | |
p | |
ranks | |
Spectral characterizations | |
Graphs with few eigenvalues | |
References | |
Author Index | |
Subject Index | |
ISBN: | 9781461419396 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory |
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Call number: | SPRINGER-2012-9781461412311:ONLINE Show nearby items on shelf |
Title: | Representing Finite Groups [electronic resource] : A Semisimple Introduction |
Author(s): |
Ambar N Sengupta |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples withdevelopment of general and pow erful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups.The text progressessystematically and the presentation is friendly and inviting. Cent ral concepts are revisited and exploredfrom multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: ASemisimple Introduction would serve as a textbook for graduate and some advanced undergraduate c ourses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A finalchapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematic s and mathematical physics will also find this book useful. A separate solutions manual is available for instructors |
Note: | Springer eBooks |
ISBN: | 9781461412311 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Quantum theory |
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Call number: | SPRINGER-2012-9781461407768:ONLINE Show nearby items on shelf |
Title: | Representation Theory of Finite Groups [electronic resource] : An Introductory Approach |
Author(s): |
Benjamin Steinberg |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linearalgebra, group theory, a nd very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted.Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside'spq-theorem and the dimension theorem, permutation representations, indu ced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probabilityand statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate theusefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exerci ses add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearlyshown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathema tics, engineering, and physics, to name a few. Its primary intended use is as a one semestertextbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a ref erence to researchers in all areas of mathematics, statistics, andseveral mathematical sciences |
Note: | Springer eBooks |
ISBN: | 9781461407768 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9781461407096:ONLINE Show nearby items on shelf |
Title: | Buildings, Finite Geometries and Groups [electronic resource] : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010 |
Author(s): |
N.S. Narasimha Sastry |
Date: | 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on Buildings, Finite Geometries and Groups organized at the Indian Statistical Institute, Bangalore, from August 29 31,2010. These contributors include so me of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lietheory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on currentdevelopments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields |
Note: | Springer eBooks |
Contents: | 1. On Characterizing Designs By Their Codes (B. Bagchi) |
2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen) | |
3. Properties of a 27 | |
dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow) | |
4. On the Geometry of Global Function Fields, the Riemann | |
Roch Theorem, and Finiteness Properties of S | |
arithmetic Groups (R. Gramlich) | |
5. Some Remarks on Two | |
Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lbeck) | |
6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji) | |
7. On Isotypies Between Galois Conj | |
ISBN: | 9781461407096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics, 2190-5614 : v10 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9781447123538:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Signal and Image Analysis and Representation [electronic resource] |
Author(s): |
Luc Florack Remco Duits Geurt Jongbloed Marie-Colette Lieshout Laurie Davies |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living onan n-dimensional smo oth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. Incontrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed forthe sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interestedin the fundamental methodology per se. Covering many topics at the forefront of curre nt research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduatestudents and researchers in the fields of computer vision, medical imaging and visual perception |
Note: | Springer eBooks |
Contents: | A Short Introduction to Diffusion |
like Methods | |
Adaptive Filtering using Channel Representations | |
3D | |
Coherence | |
Enhancing Diffusion Filtering for Matrix Fields | |
Structural Adaptive Smoothing: Principles and Applications in Imaging | |
SPD Tensors Regularization via Iwasawa Decomposition | |
Sparse Representation of Video Data by Adaptive Tetrahedralizations | |
Continuous Diffusion Wavelet Transforms and Scale Space over Euclidean Spaces and Noncommutative Lie Groups | |
Left Invariant Evolution Equations on Gabor Transforms | |
Scale Space Representations Locally Adapted to the Geometry of Ba | |
ISBN: | 9781447123538 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Computational Imaging and Vision, 1381-6446 : v41 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision |
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Call number: | SPRINGER-2012-9780817648176:ONLINE Show nearby items on shelf |
Title: | Representation Theory, Complex Analysis, and Integral Geometry [electronic resource] |
Author(s): |
Bernhard Krtz Omer Offen Eitan Sayag |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an outgrowth of the special term Harmonic Analysis, Representation Theory, and Integral Geometry, held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonnduring the summer of 2007. The contributions in the volume provide a window into a variety of subjects related to reductive groups: real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, geometry offlag varieties, restriction theory of representations, modern aspects of special functions, multiple Dirichlet series, and unfolding identities in the theory of automorphic forms. Throughout the work, great emphasis was placed onmaking the articles accessible to interested newcomers to these fields and gradu ate students. Representation Theory, Complex Analysis, and Integral Geometry aims to stimulate future research in these areas. Contributors: J. Bernstein,G. Chinta, D. Ciubotaru, J. Faraut, S. Gindikin, J. Jorgenson, J. Kramer, B. Krtz, Y.A. Neretin, K. N ishiyama, O. Offen, H. Schlichtkrull, M.J. Slupinski, R.J. Stanton, B. Speh, P.E. Trapa, T.N.Venkataramana |
Note: | Springer eBooks |
Contents: | Preface |
On Function Spaces on Symmetric Spaces | |
A Relation Involving RankinSelberg L | |
Functions of Cusp Forms and Maass Forms | |
Orthogonal Period of a Gl3(Z) Eisenstein Series | |
Regular Orbits of Symmetric Subgroups on Partial Flag Varieties | |
Helgason's Conjecture in Complex Analytical Interior | |
Lectures on Lie Algebras | |
SteinSahi Complementary Series and Their Degenerations | |
The Special Symplectic Structure of Binary Cubics | |
On the Restriction of Representations of Sl(2C) to Sl(2,R) | |
Asymptotics of Spherical Functions for Large Rank: An Introduction | |
ISBN: | 9780817648176 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Number theory |
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Call number: | SPRINGER-2011-9789400719170:ONLINE Show nearby items on shelf |
Title: | Wave Equations in Higher Dimensions [electronic resource] |
Author(s): |
Shi-Hai Dong |
Date: | 2011 |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory andRelativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the readers disposal. Acomprehensive description of quantum wave equations in highe r dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanicstextbooks and gives scientists a fresh outlook on quantum systems in all branches of phy sics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higherdimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativis tic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem andthe generalized hypervirial theorem in higher dimensions, the Schrdinger equation with position-dependent mass and the Kaluza-Klei n theory in higher dimensions are investigated. In this context, the dependence of the energy levels onthe dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography |
Note: | Springer eBooks |
Contents: | Part I (Introduction) |
Part II (Theory) | |
2. Special orthogonal groups (Introduction Abstract groupsOrthogonal group SO(n) Tensor representations of the SO(n) \Gamma matrix groups Spinor representations of the SO(n) Concluding remarks) | |
3. Rotational symmetry and Schrdinger equation in N | |
dimensional space (Introduction Rotation operator Orbital angular momentum operators The linear momentum operatorsRadial momentum operator Spherical harmonic polynomials Schrdinger equation for a two | |
body system Concluding remarks) | |
4. Dirac equation in higher dimensions (Introduction | |
ISBN: | 9789400719170 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Functional equations , Quantum theory |
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Call number: | SPRINGER-2011-9783642217449:ONLINE Show nearby items on shelf |
Title: | Supersymmetry in Mathematics and Physics [electronic resource] : UCLA Los Angeles, USA 2010 |
Author(s): |
Sergio Ferrara Rita Fioresi V.S Varadarajan |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new developmentin geometry, and mat hematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of thevarious questions raised |
Note: | Springer eBooks |
Contents: | Introduction |
Black Holes and First Order Flows in Supergravity | |
Representations of Super Lie Groups: Some Remarks | |
On Chiral Quantum Superspaces | |
On the Construction of Chevalley Supergroup | |
Indecomposable Finite | |
dimensional Representations of a Class o f Lie algebras and Lie Superalgebras | |
On the Geometry of Super Riemann Surfaces | |
Charge Orbits and Moduli Spaces of Black Hole Attractors | |
Maximal Supersymmetry | |
Lie Supergroups, Unitary Representations, and Invariant Cones | |
Geometry of Dual Pairs of Complex Supercurves | |
On the Superdimension of an Irreducible Representat | |
ISBN: | 9783642217449 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2027 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Geometry , Mathematical physics |
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Call number: | SPRINGER-2011-9783642174049:ONLINE Show nearby items on shelf |
Title: | Modular Invariant Theory [electronic resource] |
Author(s): |
H.E.A. Eddy Campbell David L Wehlau |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classicalnon-modular case, and it descri bes many open questions. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the betterunderstood non-modular setting. It details techniques f or the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of manytopics as well as a quick survey of the elements of algebraic geometry and com mutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchersan introduction to many important topics inmodern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter |
Note: | Springer eBooks |
Contents: | 1 First Steps |
2 Elements of Algebraic Geometry and Commutative Algebra | |
3 Applications of Commutative Algebra to Invariant Theory | |
4 Examples | |
5 Monomial Orderings and SAGBI Bases | |
6 Block Bases | |
7 The Cyclic Group Cp | |
8 Polynomial Invariant Rings | |
9 The Transfer | |
10 Invariant Rings via Localization | |
11 Rings of Invariants which are Hypersurfaces | |
12 Separating Invariants | |
13 Using SAGBI Bases to Compute Rings of Invariants | |
14 Ladders | |
References | |
Index | |
ISBN: | 9783642174049 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v139 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic |
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Call number: | SPRINGER-2011-9783642111174:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis and Group Representation [electronic resource] |
Author(s): |
A. Fig Talamanca |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lectures: A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties.- M Cowling: Unitary and uniformly bounded representations of some simple Lie groups.- M. Duflo: Construction de representations unitaires dun groupede Lie.- R. Howe: On a no tion of rank for unitary representations of the classical groups.- V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups.- R. Zimmer: Ergodic theory, group representations and rigidity.- Seminars:A. Koranyi: Some applications of Gelfand pair s in classical analysis |
Note: | Springer eBooks |
Contents: | A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties |
M Cowling: Unitary and uniformly bounded representations of some simple Lie groups | |
M. Duflo: Construction de reprsentations unitaires dun groupe de Lie | |
R. Howe: On a notion of rank for unitary representations of the classical groups | |
A. Koranyi: Some applications of Gelfand pairs in classical analysis | |
V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups | |
R. Zimmer: Ergodic theory, group representations and rigidity | |
ISBN: | 9783642111174 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v82 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Number theory |
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Call number: | SPRINGER-2011-9783642110122:ONLINE Show nearby items on shelf |
Title: | Theory of Group Representations and Fourier Analysis [electronic resource] |
Author(s): |
F Gherardelli |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A. Fig Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Reprsentations des groupes linaires p-adiques.- G.W. Mackey: Infinite-dimensional grouprepresentations and their applicati ons |
Note: | Springer eBooks |
Contents: | A. Fig Talamanca: Random Fourier series on compact groups |
S. Helgason: Representations of semisimple Lie groups | |
H. Jacquet: Reprsentations des groupes linaires p | |
adiques | |
G.W. Mackey: Infinite | |
dimensional group representations and their applications | |
ISBN: | 9783642110122 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v53 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups |
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Call number: | SPRINGER-2011-9781441960559:ONLINE Show nearby items on shelf |
Title: | Integral Geometry and Radon Transforms [electronic resource] |
Author(s): |
Sigurdur Helgason |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this text, integral geometry deals with Radons problem of representing a function on a manifold in terms of its integrals over certain submanifoldshence the term the Radon transform. Examples and far-reachinggeneralizations lead to fundamental pro blems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case ofthe plane, the inversion theorem and the support theorem ha ve had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroomuse or self-study. A number of exercises point to further results with document ation. From the reviews: Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book isconcentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area. Boris Rubin,Louisiana State University |
Note: | Springer eBooks |
Contents: | The Radon Transformon Rn |
A Duality in Integral Geometry | |
The Radon Transform on Two | |
Point Homogeneous Spaces | |
The X | |
Ray Transform on a Symmetric Space | |
Orbital Integrals | |
The Mean | |
Value Operator | |
Fourier Transforms and Distribution: A Rapid Course | |
Lie Transformation Groups and Differential Operators | |
Bibliography | |
Notational Conventions | |
Index | |
ISBN: | 9781441960559 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Integral Transforms , Global differential geometry |
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Call number: | SPRINGER-2011-9780857297167:ONLINE Show nearby items on shelf |
Title: | Representations of Hecke Algebras at Roots of Unity [electronic resource] |
Author(s): |
Meinolf Geck Nicolas Jacon |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest it is one that has also seen a number of breakthroughs in recent years. Inclassifying the irreduci ble representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory ofcells, the authors develop an analogue of James' (1970) characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Heckealgebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theoryof affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by a n interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, thecombinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of thefield with an interest in Hecke algebras |
Note: | Springer eBooks |
Contents: | Generic IwahoriHecke algebras |
KazhdanLusztig cells and cellular bases | |
Specialisations and decomposition maps | |
Hecke algebras and finite groups of Lie type | |
Representation theory of ArikiKoike algebras | |
Canonical bases in affine type A and Arikis theorem | |
Decomposition numbers for exceptional types | |
ISBN: | 9780857297167 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications : v15 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2011-9780857291578:ONLINE Show nearby items on shelf |
Title: | Representations of SL2(Fq) [electronic resource] |
Author(s): |
Cdric Bonnaf |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory inthe general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provide the simplicity required for a complete description of the theory, but also the richness needed forillustrating the most delicate aspects. The developm ent of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory.To this end, the author makes use of fundamental results of l-adic cohomol ogy. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, withparticular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. Withthe provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well asresearchers and lecturers with an interest in Deligne-Lusztig theory |
Note: | Springer eBooks |
Contents: | Part I Preliminaries |
Structure of SL2(Fq) | |
The Geometry of the Drinfeld Curve | |
Part II Ordinary Characters | |
Harish | |
Chandra Induction | |
Deligne | |
Lusztig Induction | |
The Character Table | |
Part III Modular Representations | |
More about Characters of G and of its Sylow Subgroups | |
Unequal Characteristic: Generalities | |
Unequal Characteristic: Equivalences of Categories | |
Unequal Characteristic: Simple Modules, Decomposition Matrices | |
Equal Characteristic | |
Part IV Complements | |
Special Cases | |
Deligne | |
Lusztig Theory: an Overview | |
Part V Appendices | |
A l | |
Adic Cohomology | |
B B | |
ISBN: | 9780857291578 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications : v13 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Group theory |
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Call number: | SPRINGER-2011-9780817647414:ONLINE Show nearby items on shelf |
Title: | Developments and Trends in Infinite-Dimensional Lie Theory [electronic resource] |
Author(s): |
Karl-Hermann Neeb Arturo Pianzola |
Date: | 2011 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts:infinite-dimensional Lie ( super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representationtheory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and KacMoody superalgebras.The articles in Part (B) examine connections between infinite-dimension al Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, toJordan-theoretic geometries and new results on direct-limit groups. The analytic representation theor y of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods basedon heat kernels, multiplicity freeness, BanachLiePoisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Belti, W. Bertram, J. Faulkner, Ph. Gille, H. Glckner, K.-H.Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf |
Note: | Springer eBooks |
Contents: | Preface |
Part A: Infinite | |
Dimensional Lie (Super | |
)Algebras | |
Isotopy for Extended Affine Lie Algebras and Lie Tori | |
Remarks on the Isotriviality of Multiloop Algebras | |
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras A Survey | |
Tensor Representations of Classical Locally Finite Lie Algebras | |
Lie Algebras, Vertex Algebras, and Automorphic Forms | |
KacMoody Superalgebras and Integrability | |
Part B: Geometry of Infinite | |
Dimensional Lie (Transformation) Groups | |
Jordan Structures and Non | |
Associative Geometry | |
Direct Limits of Infinite | |
Dimensional L | |
ISBN: | 9780817647414 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v288 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Group theory , Topological Groups , Geometry |
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Call number: | SPRINGER-2010-9783642112973:ONLINE Show nearby items on shelf |
Title: | Biset Functors for Finite Groups [electronic resource] |
Author(s): |
Serge Bouc |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics onbiset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted tobiset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors tolong-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting ofadvanced results in the area, with some new ideas and proofs |
Note: | Springer eBooks |
Contents: | 1 Examples |
Part I General properties | |
2 G | |
sets and (H,G) | |
bisets | |
3 Biset functors | |
4 Simple functors | |
Part II Biset functors on replete subcategories | |
5 The Burnside functor | |
6 Endomorphism algebras | |
7 The functor CRC | |
8 Tensor product and internal hom | |
Part III p | |
biset functors | |
9 Rational representations of p | |
groups | |
10 p | |
biset functors | |
11 Applications | |
12 The Dade group | |
ISBN: | 9783642112973 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1990 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , K-theory |
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Call number: | SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf |
Title: | Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures |
Author(s): |
Leonid Positselski |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
0 Preliminaries and Summary | |
1 Semialgebras and Semitensor Product | |
2 Derived Functor SemiTor | |
3 Semicontramodules and Semihomomorphisms | |
4 Derived Functor SemiExt | |
5 Comodule | |
Contramodule Correspondence | |
6 Semimodule | |
Semicontramodule Correspondence | |
7 Functoriality in the Coring | |
8 Functoriality in the Semialgebra | |
9 Closed Model Category Structures | |
10 A Construction of Semialgebras | |
11 Relative Nonhomogeneous Koszul Duality | |
Appendix A Contramodules over Coalgebras over Fields | |
Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se | |
ISBN: | 9783034604369 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry |
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Call number: | SPRINGER-2010-9783034604222:ONLINE Show nearby items on shelf |
Title: | Visions in Mathematics [electronic resource] : GAFA 2000 Special Volume, Part I |
Author(s): |
N Alon J Bourgain A Connes M Gromov V Milman |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Visions in Mathematics - Towards 2000 was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematiciansworldwide. The goals of the conf erence were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims ofthe conference are reflected in the present set of sur vey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the first part of a two-volume set that will serve anyresearch mathematician or advanced student as an overview and guideline thro ugh the multifaceted body of mathematical research in the present and near future |
Note: | Springer eBooks |
Contents: | Foreword |
Program of the Conference | |
Gauss | |
Manin determinant connections and periods of irregular connections | |
Problems in Hamiltonian PDE's | |
On a classical limit of quantum theory and the non | |
linear Hartree equation | |
Rough structure and classification | |
Spaces and questions | |
Classification of infinite | |
dimensional simple groups of supersymmetries and quantum field theory | |
Geometrization in representation theory | |
Geometric and unipotent crystals | |
y | |
functions of representations and lifting (Appendix by V. Vologodsky) | |
PDE as a unified subject | |
Lessons for turbulence | |
The | |
ISBN: | 9783034604222 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2010-9781441908988:ONLINE Show nearby items on shelf |
Title: | Operational Spacetime [electronic resource] : Interactions and Particles |
Author(s): |
Heinrich Saller |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Operational Spacetime: Interactions and Particles provides readers with a basic understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for theparametrization of op eration Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physicalproperties are related eigenvalues or invarian ts. As an explicit example, an operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge-isospin group in the general lineargroup in two complex dimensions, i.e., the Lorentz cover group, extend ed by the causal (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically,with the properties of interactions and particles as arising in the representations of its tan gent Minkowski spaces. Heinrich Saller is the author of Operational Quantum Theory I: Nonrelativistic Structures (Springer, 2006) andOperational Quantum Theory II: Relativistic Structures (Springer, 2006) |
Note: | Springer eBooks |
Contents: | Introduction and Orientation |
Einstein's Gravity | |
Riemannian Manifolds | |
Mass Points | |
Quantum Mechanics | |
Quantum Fields of Flat Spacetime | |
External and Internal Operations | |
Relativities and Homogeneous Spaces | |
Representation Coefficients | |
Convolutions and Product Representations | |
Interactions and Kernels | |
Electroweak Spacetime | |
Masses and Coupling Constants | |
ISBN: | 9781441908988 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fundamental Theories of Physics : v163 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2010-9780817649845:ONLINE Show nearby items on shelf |
Title: | Spinors in Four-Dimensional Spaces [electronic resource] |
Author(s): |
Gerardo F Torres del Castillo |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensionalspaces with any signatu re. Some of the useful applications of four-dimensional spinors, such as YangMills theory, are derived in detail using illustrative examples. Key topics and features: Uniform treatment of the spinorformalism for four-dimensional spaces of any signature, not only the usual signature (+ + + ) employed in relativity Examples taken from Riemannian geometry and special or general relativity are discussed in detail, emphasizingthe usefulness of the two-component spinor formalism Exercises in each chapter Th e relationship of Clifford algebras and Dirac four-component spinors is established Applications of the two-component formalism, focusingmainly on general relativity, are presented in the context of actual computations Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applicationsof the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tens or. This systematic and self-contained book is suitable as a seminar text, a reference book, anda self-study guide. Reviews from the author's previous book, 3-D Spinors, Spin-Weighted Functions and their Applications: In summarythe book gathers much of wh at can be done with 3-D spinors in an easy-to-read, self-contained formdesigned for applications that will supplement many available spinor treatments. The bookshould be appealing to graduate students and researchers in relativity and mathematical physics . Mathematical Reviews The present bookprovides an easy-to-read and unconventional presentation of the spinor formalism for three-dimensional spaces with a definite or inde |
Note: | Springer eBooks |
Contents: | 1 Spinor Algebra |
1.1 Orthogonal Groups | |
1.2 Null Tetrads and the Spinor Equivalent of a Tensor | |
1.3 Spinorial Representation of the Orthogonal Transformations | |
1.3.1 Euclidean Signature | |
1.3.2 Lorentzian Signature | |
1.3.3 Ultrahyperbolic Signature | |
1.4 Reflections | |
1.5 Clifford Algebra. Dirac Spinors | |
1.6 Inner Products. Mate of a Spinor | |
1.7 Principal Spinors. Algebraic Classification | |
Exercises | |
2 Connection and Curvature | |
2.1 Covariant Differentiation | |
2.2 Curvature | |
2.2.1 Curvature Spinors | |
2.2.2 Algebraic Classification of the Conformal Curvature | |
2.3 Conformal Rescalings | |
2.4 Killing | |
ISBN: | 9780817649845 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v59 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf |
Title: | Representation Theory and Complex Geometry [electronic resource] |
Author(s): |
Neil Chriss Victor Ginzburg |
Date: | 2010 |
Edition: | 1st |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews |
Note: | Springer eBooks |
Contents: | Preface |
Chapter 0. Introduction | |
Chapter 1. Symplectic Geometry | |
Chapter 2. Mosaic | |
Chapter 3. Complex Semisimple Groups | |
Chapter 4. Springer Theory | |
Chapter 5. Equivariant K | |
Theory | |
Chapter 6. Flag Varieties, K | |
Theory, and Harmonic Polynomials | |
Chapter 7. Hecke Algebras and K | |
Theory | |
Chapter 8. Representations of Convolution Algebras | |
Bibliography | |
ISBN: | 9780817649388 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics |
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Call number: | SPRINGER-2010-9780817649326:ONLINE Show nearby items on shelf |
Title: | Topics in Operator Semigroups [electronic resource] |
Author(s): |
Shmuel Kantorovitz |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics suchas Markov processes, th e abstract Cauchy problem, evolution equations, and mathematical physics. This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectraltheory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications. Topics include: * TheHilleYosida and LumerPhillips characterizations of semigroup generators * Th e TrotterKato approximation theorem * Katos unified treatment of the exponential formula and the Trotter product formula * The HillePhillipsperturbation theorem, and Stones representation of unitary semigroups * Generalizations of spectral theorys connect ion to operator semigroups * A natural generalization of Stones spectral integral representation to a Banachspace setting With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operatorsemigroups |
Note: | Springer eBooks |
Contents: | General Theory |
Basic Theory | |
The Semi | |
Simplicity Space for Groups | |
Analyticity | |
The Semigroup as a Function of its Generator | |
Large Parameter | |
Boundary Values | |
Pre | |
Semigroups | |
Integral Representations | |
The Semi | |
Simplicity Space | |
The LaplaceStieltjes Space | |
Families of Unbounded Symmetric Operators | |
A Taste of Applications | |
Analytic Families of Evolution Systems | |
Similarity | |
ISBN: | 9780817649326 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v281 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Operator theory |
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Call number: | SPRINGER-2010-9780817648756:ONLINE Show nearby items on shelf |
Title: | Symmetry and Spaces [electronic resource] : In Honor of Gerry Schwarz |
Author(s): |
H. E. A Campbell Aloysius G Helminck Hanspeter Kraft David Wehlau |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A group of Gerry Schwarzs colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the widerange of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts,with a particular focus on characteristic 0 and mo dular invariant theory. Contributors: M. Brion A. Broer D. Daigle J. Elmer P. Fleischmann G. Freudenberg D. Greb P. Heinzner A. Helminck B. Kostant H. Kraft R. J. Shank W. Traves N. R.Wallach D. Wehlau |
Note: | Springer eBooks |
Contents: | Some Basic Results on Actions of Nonaffine Algebraic Groups |
On ChevalleyShephardTodds Theorem in Positive Characteristic | |
Families of Affine Fibrations | |
On the Depth of Modular Invariant Rings for the Groups | |
Khlerian Reduction in Steps | |
On Orbit Decompositions for Symmetric | |
Varieties | |
Root Systems for Levi Factors and Borelde Siebenthal Theory | |
Polarizations and Nullcone of Representations of Reductive Groups | |
Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups | |
Differential Operators on Grassmann Varieties | |
ISBN: | 9780817648756 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v278 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Field theory (Physics) |
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Call number: | SPRINGER-2010-9780817646974:ONLINE Show nearby items on shelf |
Title: | Representation Theory of Algebraic Groups and Quantum Groups [electronic resource] |
Author(s): |
Akihiko Gyoja Hiraku Nakajima Ken-ichi Shinoda Toshiaki Shoji Toshiyuki Tanisaki |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras,representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection groups and associated Hecke algebras. Representation Theory of Algebraic Groups andQuantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors: H. H. Andersen, S. Ariki, C. Bonnaf, J. Chuang, J. Du, M.Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. La m, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang |
Note: | Springer eBooks |
ISBN: | 9780817646974 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v284 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Algebra , Topological Groups , Number theory , Mathematical physics |
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Call number: | SPRINGER-2010-9780387788661:ONLINE Show nearby items on shelf |
Title: | Groups and Symmetries [electronic resource] : From Finite Groups to Lie Groups |
Author(s): |
Yvette Kosmann-Schwarzbach |
Date: | 2010 |
Edition: | First |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: Brisk review of the basicdefinitions of group theory, wi th examples Representation theory of finite groups: character theory Representations of compact groups using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) andSU(2), and their representations Spherical harmonics Represen tations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraitsand a few historical remarks. With only linear algebra and calculus as prerequisites, Grou ps and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be ofinterest to beginning graduate students. Exercises for each chapter and a collection of problems with complete sol utions make this an ideal text for the classroom and for independent study |
Note: | Springer eBooks |
Contents: | Introduction |
Acknowledgments | |
General Facts about Groups | |
Representations of Finite Groups | |
Representations of Compact Groups | |
Lie Groups and Lie Algebras | |
Lie groups SU(2) and SO(3) | |
Representations of SU(2) and SO(3) | |
Spherical Harmonics | |
Representations of SU(3) and Quarks | |
Problems and Solutions | |
Bibliography | |
Index | |
ISBN: | 9780387788661 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Quantum theory , Crystallography |
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Location: | ONLINE |
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