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Call number: | 9783319297347:ONLINE Show nearby items on shelf |
Title: | Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories |
Author(s): |
Eckehard W Mielke |
Date: | 2017 |
Edition: | 2nd ed. 2017 |
Size: | 1 online resource (XVII, 373 p. 18 illus., 8 illus. in color p.) |
Contents: | Preface -- 1 Historical background -- 2 Geometry of gauge fields -- 3 Maxwell and Yang-Mills theory -- 4 Gravitation as a gauge theory -- 5 Einstein-Cartan theory -- 6 Teleparallelism -- 7 Yang’s theory of gravity -- 8 BRST |
quantization of gravity -- 9 Gravitational instantons -- 10 Three-dimensional gravity -- 11 Spinor bundles -- 12 Chiral anomalies -- 13 Topological SL(5R) gauge invariant action -- 14 Geometrodynamics and its extensions -- 15 Color | |
Geometrodynamics -- 16 Geometrodynamical model of quark confinement?- Appendix A Notation and mathematical terms -- Appendix B Calculus of exterior forms -- Appendix C Lie groups | |
ISBN: | 9783319297347 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Mathematical physics , Gravitation , Elementary particles (Physics) , Quantum field theory , Physics , Classical and Quantum Gravitation, Relativity Theory , Mathematical Physics , Elementary Particles, Quantum Field Theory |
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Call number: | SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf |
Title: | Manifolds, Sheaves, and Cohomology |
Author(s): |
Torsten Wedhorn |
Date: | 2016 |
Size: | 1 online resource (354 p.) |
Note: | 10.1007/978-3-658-10633-1 |
Contents: | Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis |
ISBN: | 9783658106331 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf |
Title: | Extensions of Positive Definite Functions Applications and Their Harmonic Analysis |
Author(s): |
Palle Jorgensen |
Date: | 2016 |
Size: | 1 online resource (9 p.) |
Note: | 10.1007/978-3-319-39780-1 |
ISBN: | 9783319397801 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2160 |
Keywords: | Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes |
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Call number: | SPRINGER-2016-9783319392868:ONLINE Show nearby items on shelf |
Title: | Operator Algebras and Applications The Abel Symposium 2015 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (2 p.) |
Note: | 10.1007/978-3-319-39286-8 |
Contents: | C*-tensor categories and subfactors for totally disconnected groups: Y. Arano and S. Vaes -- Decomposable approximations revisited: N.P. Brown, J.R. Carrión and S. White -- Exotic crossed products: A. Buss, S. Echterhoff, and R. Willett -- On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra: T. M. Carlsen and A. Sims -- Commutator inequalities via Schur products: E. Christensen -- C*-algebras associated with algebraic actions: J. Cuntz -- A new look at C*-simplicit y and the unique trace property of a group: U. Haagerup -- Equilibrium states on graph algebras: A. an Huef and I. Raeburn -- Semigroup C_-algebras: X. Li -- Topological full groups of étale groupoids: H. Matui -- Towards a classification of compact quan tum groups of Lie type: S. Neshveyev and M. Yamashita -- A homology theory for Smale spaces: a summary: I.F. Putnam -- On the positive eigenvalues and eigenvectors of a non-negative matrix: K. Thomsen -- Classification of graph algebras: a |
selective survey: M. Tomforde -- QDQ vs. UCT: W. Winter | |
ISBN: | 9783319392868 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Abel Symposia: 12 |
Keywords: | Mathematics , K-theory , Dynamics , Ergodic theory , Functional analysis , Mathematical physics , Mathematics , Functional Analysis , Dynamical Systems and Ergodic Theory , K-Theory , Mathematical Physics |
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Call number: | SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf |
Title: | Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014 |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (332 p.) |
Note: | 10.1007/978-3-319-30451-9 |
ISBN: | 9783319304519 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 159 |
Keywords: | Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups |
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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-2014-9788132215998:ONLINE Show nearby items on shelf |
Title: | Basic Modern Algebra with Applications [electronic resource] |
Author(s): |
Mahima Ranjan Adhikari Avishek Adhikari |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource |
Contents: | Prerequisites: Basics of Set Theory and Integers |
Groups: Introductory Concepts | |
Actions of Groups, Topological Groups and semigroups | |
Rings: Introductory Concepts | |
Ideals of Rings: Introductory concepts | |
Factorization in Integral Domains and in Polynomial Rings | |
Rings with Chain Conditions | |
Vector Spaces | |
Modules | |
Algebraic Aspects of Number Theory | |
Algebraic Numbers | |
Introduction to Mathematical Cryptography | |
Appendix A: Some Aspects of Semirings | |
Appendix B: Category Theory | |
Appendix C: A Brief Historical Note | |
ISBN: | 9788132215998 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Number theory |
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Call number: | SPRINGER-2014-9783642553615:ONLINE Show nearby items on shelf |
Title: | Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011 |
Author(s): |
Abdenacer Makhlouf Eugen Paal Sergei D Silvestrov Alexander Stolin |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students |
Contents: | Part I Algebra |
Part II Geometry | |
Part III Dynamical Symmetries and Conservation Laws | |
Part IV Mathematical Physics and Applications | |
ISBN: | 9783642553615 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics |
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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-2014-9781493909384: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-2013-9789400753457:ONLINE Show nearby items on shelf |
Title: | Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems |
Author(s): |
Gerd Rudolph Matthias Schmidt |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact |
Note: | Springer eBooks |
Contents: | 1 Differentiable manifolds |
2 Vector bundles | |
3 Vector fields | |
4 Differential forms | |
5 Lie groups | |
6 Lie group actions | |
7 Linear symplectic algebra | |
8 Symplectic geometry | |
9 Hamiltonian systems | |
10 Symmetries | |
11 Integrability | |
12 Hamilton | |
Jacobi theory | |
References | |
ISBN: | 9789400753457 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics |
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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-2013-9783642362163:ONLINE Show nearby items on shelf |
Title: | Clifford Algebras and Lie Theory [electronic resource] |
Author(s): |
Eckhard Meinrenken |
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 monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results onsymmetric bilinear form s and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes apresentation of Petraccis proof of the PoincarBirk hoffWitt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lietheory include Duflos theorem for the case of quadratic Lie algebras, multiplets of rep resentations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over asemisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fa scinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principalsl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Cliffor d theory, relevant for students and researchers in mathematics andphysics |
Note: | Springer eBooks |
Contents: | Preface |
Conventions | |
List of Symbols | |
1 Symmetric bilinear forms | |
2 Clifford algebras | |
3 The spin representation | |
4 Covariant and contravariant spinors | |
5 Enveloping algebras | |
6 Weil algebras | |
7 Quantum Weil algebras | |
8 Applications to reductive Lie algebras | |
9 D(g k) as a geometric Dirac operator | |
10 The HopfKoszulSamelson Theorem | |
11 The Clifford algebra of a reductive Lie algebra | |
A Graded and filtered super spaces | |
B Reductive Lie algebras | |
C Background on Lie groups | |
References | |
Index | |
ISBN: | 9783642362163 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Mathematical physics |
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Call number: | SPRINGER-2013-9783642310904:ONLINE Show nearby items on shelf |
Title: | Poisson Structures [electronic resource] |
Author(s): |
Camille Laurent-Gengoux Anne Pichereau Pol Vanhaecke |
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: | Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures |
Note: | Springer eBooks |
Contents: | Part I Theoretical Background:1.Poisson Structures: Basic Definitions |
2.Poisson Structures: Basic Constructions | |
3.Multi | |
Derivations and Khler Forms | |
4.Poisson (Co)Homology | |
5.Reduction | |
Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds | |
7.Linear Poisson Structures and Lie Algebras | |
8.Higher Degree Poisson Structures | |
9.Poisson Structures in Dimensions Two and Three | |
10.R | |
Brackets and r | |
Brackets | |
11.PoissonLie Groups | |
Part III Applications:12.Liouville Integrable Systems | |
13.Deformation Quantization | |
A Multilinear Algebra | |
B Real | |
ISBN: | 9783642310904 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry |
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Call number: | SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource] |
Author(s): |
Shahla Molahajloo Stevan Pilipovi Joachim Toft M. W Wong |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series |
Note: | Springer eBooks |
Contents: | Preface |
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds | |
The Singular Functions of Branching Edge Asymptotics | |
The Heat Kernel and Green Function of the Sub | |
Laplacian on the Heisenberg Group | |
Metaplectic Equivalence of the Hierarchical Twisted Laplacian | |
The Heat Kernel and Green Function of a Sub | |
Laplacian on the Hierarchical Heisenberg Group | |
Lp | |
Bounds for Pseudo | |
Differential Operators on the Torus | |
Multiplication Properties in Gelfand | |
Shilov Pseudo | |
Differential Calculus | |
Operator Invariance | |
Initial Value Problems in the Time | |
Frequency Do | |
ISBN: | 9783034805858 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v231 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial |
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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-2013-9780817683856:ONLINE Show nearby items on shelf |
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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
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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Call number: | SPRINGER-2013-9780817683641:ONLINE Show nearby items on shelf |
Title: | Configurations from a Graphical Viewpoint [electronic resource] |
Author(s): |
Toma Pisanski Brigitte Servatius |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. Inthis self-contained tex tbook, algebraic graph theory is used to introduce groups topological graph theory is used to explore surfaces and geometric graph theory is implemented to analyze incidence geometries. After a preview ofconfigurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied.Geometric aspects, some historical remarks, references, and applicationsof classicalconfigurationsappear in the last chapter. With over two hundred illustrations, challenging exercises at t he end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint iswell suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicia ns and researchers |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Graphs | |
Groups, Actions, and Symmetry | |
Maps | |
Combinatorial Configurations | |
Geometric Configurations | |
Index | |
Bibliography | |
ISBN: | 9780817683641 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Birkhuser Advanced Texts Basler Lehrbcher |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Combinatorics , Geometry , Topology |
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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 |
Note: | Springer 2013 e-book collections |
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-2012-9783642227165:ONLINE Show nearby items on shelf |
Title: | The Schringer-Virasoro Algebra [electronic resource] |
Author(s): |
Jie Unterberger Claude Roger |
Date: | 2012 |
Publisher: | Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Monograph |
Note: | Springer 2012 Physics and Astronomy eBook collection |
Note: | Springer e-book platform |
ISBN: | 9783642227165 |
Series: | Texts and Monographs in Physics |
Series: | e-books |
Keywords: | Mathematical Methods in Physics , Topological Groups, Lie Groups , Mathematical Physics , Category Theory, Homological Algebra , Statistical Physics, Dynamical Systems and Complexity |
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Call number: | SPRINGER-2012-9783642225970:ONLINE Show nearby items on shelf |
Title: | Topics in Noncommutative Algebra [electronic resource] : The Theorem of Campbell, Baker, Hausdorff and Dynkin |
Author(s): |
Andrea Bonfiglioli Roberta Fulci |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, NumericalAnalysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra ornot) to understand and apply the statements and numero us corollaries of the main result 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view andnotation 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincar, Pascal, Campbell, Baker, Hausdorff and Dynkin 4) give an outlook on theapplications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) 5 ) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modernliterature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems an d applications. The book assumes some undergraduate-level knowledge of algebra and analysis,but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool fo r beginners in Algebra |
Note: | Springer eBooks |
Contents: | 1 Historical Overview |
Part I Algebraic Proofs of the CBHD Theorem | |
2 Background Algebra | |
3 The Main Proof of the CBHD Theorem | |
4 Some Short Proofs of the CBHD Theorem | |
5 Convergence and Associativity for the CBHD Theorem | |
6 CBHD, PBW and the Free Lie Algebras | |
Part II Proofs of the Algebraic Prerequisites | |
7 Proofs of the Algebraic Prerequisites | |
8 Construction of Free Lie Algebras | |
9 Formal Power Series in One Indeterminate | |
10 Symmetric Algebra | |
ISBN: | 9783642225970 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2034 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry |
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Call number: | SPRINGER-2012-9780817682743:ONLINE Show nearby items on shelf |
Title: | Highlights in Lie Algebraic Methods [electronic resource] |
Author(s): |
Anthony Joseph Anna Melnikov Ivan Penkov |
Date: | 2012 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | An outgrowth of a two-week summer sessionat Jacobs University inBremen, Germany in August 2009 (Structures in Lie Theory, Crystals, Derived Functors, HarishChandra Modules, Invariants and Quivers), this volume consistsof expository and research artic les that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and KacMoody Lie algebras, modularrepresentations, primitive ideals, representation theory of Arti n algebras and quivers, KacMoody superalgebras, categories of HarishChandra modules, cohomological methods, and cluster algebras. List of Contributors: M. BoosM. Brion J. Fuchs M. Gorelik A. Joseph M. Reineke C. Schweigert V. Serganova A. Seven W. Soergel B. Wilson G. Zuckerman |
Note: | Springer eBooks |
Contents: | Preface |
Part I: The Courses | |
1 Spherical Varieties | |
2 Consequences of the Littelmann Path Model for the Structure of the Kashiwara B() Crystal | |
3 Structure and Representation Theory of KacMoody Superalgebras | |
4 Categories of HarishChandra Modules | |
5 Generalized HarishChandra Modules | |
Part II: The Papers | |
6 B | |
Orbits of 2 | |
Nilpotent Matrices | |
7 The Weyl Denominator Identity for Finite | |
Dimensional Lie Superalgebras | |
8 Hopf Algebras and Frobenius Algebras in Finite Tensor Categories | |
9 Mutation Classes of 3 x 3 Generalized Cartan Matrices | |
10 Contractions and Po | |
ISBN: | 9780817682743 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v295 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Matrix theory , Topological Groups |
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Call number: | SPRINGER-2012-9780817682712:ONLINE Show nearby items on shelf |
Title: | Differentiable Manifolds [electronic resource] : A Theoretical Physics Approach |
Author(s): |
Gerardo F Torres del Castillo |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The works first three chaptersintroduce the basic concep ts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequentlyemployed in the study of differential equations ( Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked outin detail, as well as exercises intended to show how the formalism is a pplied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduateor beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics |
Note: | Springer eBooks |
Contents: | Preface |
1 Manifolds | |
2 Lie Derivatives | |
3 Differential Forms | |
4 Integral Manifolds | |
5 Connections | |
6. Riemannian Manifolds | |
7 Lie Groups | |
8 Hamiltonian Classical Mechanics | |
References | |
Index | |
ISBN: | 9780817682712 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Cell aggregation Mathematics , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2012-9780817649449:ONLINE Show nearby items on shelf |
Title: | Stochastic Models, Information Theory, and Lie Groups, Volume 2 [electronic resource] : Analytic Methods and Modern Applications |
Author(s): |
Gregory S Chirikjian |
Date: | 2012 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges betweenfields that are rarely stu died by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, andgroup-theoretic concepts in the modeling of physical p henomena. Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, andthe probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statisticalanalysis, and error propagation on Lie groups. Key features and topics of Volume 2: * The author reviews the concept ofandfunctions and integration onLie groups with many concrete examples. * Extensive exercises andmotivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes on Lie groups or geometric aspects of probability and statistics. *Specific application areas are explored,including biomolecular statistical mechanics and information-driven motion in robotics. * The concrete presentation style makes it easy for readers to obtain numeri cal solutions for their own problems the emphasis is on how tocalculate quantities rather than how to prove theorems. * Modern problems at the interface of mechanics, control theory, and communications are handled in a unified framework and multiple direc tions for future research are explored.Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practition |
Note: | Springer eBooks |
Contents: | Lie Groups I: Introduction and Examples |
Lie Groups II: Differential Geometric Properties | |
Lie Groups III: Integration, Convolution, and Fourier Analysis | |
Variational Calculus on Lie Groups | |
Statistical Mechanics and Ergodic Theory | |
Parts Entropy and the Principal Kinematic Formula | |
Estimation and Multivariate Analysis in R^n | |
Information, Communication, and Group Therapy | |
Algebraic and Geometric Coding Theory | |
Information Theory on Lie Groups | |
Stochastic Processes on Lie Groups | |
Locomotion and Perception as Communication over Principal Fiber Bundles and A Survey of Addi | |
ISBN: | 9780817649449 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied and Numerical Harmonic Analysis |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global differential geometry , Distribution (Probability theory) , Mathematical physics , Engineering mathematics |
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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-2012-9780387847948:ONLINE Show nearby items on shelf |
Title: | Structure and Geometry of Lie Groups [electronic resource] |
Author(s): |
Joachim Hilgert Karl-Hermann Neeb |
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 text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.Building onthe authors' Lie-Gruppen undLie-Algebren textbook from 1991, itp resents the fundamental principles of Lie groupswhile incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometryin the field. The text is entirely self contained,and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretelyand directly illustratethe correspondence between groups and their Lie algebras. In the second part of the book, theauthorsinvestigate the basic structure and representation theory of finite dimensional Lie algebras,suchasthe rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (ro ot decompositions), and questions related to representation theory. In the third part of the book, the authorsturn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, thefourth part of the book deals with th e structure theory of Lie groups, includingsome refined applications of theexponential function, various classes of Lie groups, andstructural issues for general Lie groups. To round out the book's content, several appendices appear at the end of thislast part. Containing a wealth of useful information,including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups andis a valuable addition to the literature. Prerequisites are generally kept to a minimum , and various pedagogicalfeatures make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more adva |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction | |
Part I Matrix Groups | |
2 Concrete Matrix Groups | |
3The Matrix Exponential Function | |
4Linear Lie Groups | |
Part II Lie Algebras | |
5Elementary Structure Theory of Lie Algebras | |
6Root Decomposition | |
7Representation Theory of Lie Algebras | |
Part III Manifolds and Lie Groups | |
8 Smooth Manifolds | |
9 Basic Lie Theory | |
10 Smooth Actions of Lie Groups | |
Part IV Structure Theory of Lie Groups | |
11 Normal Subgroups, Nilpotemt and Solvable Lie Groups | |
12 Compact Lie Groups | |
13 Semisimple Lie Groups | |
14 General Structure Theory | |
15 Complex Lie | |
ISBN: | 9780387847948 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Algebraic topology |
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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-2011-9783642211478:ONLINE Show nearby items on shelf |
Title: | p-Adic Lie Groups [electronic resource] |
Author(s): |
Peter Schneider |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with aself-contained and detailed intr oduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets upthe analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition ofLazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings |
Note: | Springer eBooks |
Contents: | Introduction |
Part A: p | |
Adic Analysis and Lie Groups | |
I.Foundations | |
I.1.Ultrametric Spaces | |
I.2.Nonarchimedean Fields | |
I.3.Convergent Series | |
I.4.Differentiability | |
I.5.Power Series | |
I.6.Locally Analytic Functions | |
II.Manifolds | |
II.7.Charts and Atlases | |
II.8.Manifolds | |
II.9.The Tangent Space | |
II.10.The Topological Vector Space C^an(M,E), part 1 | |
II.11 Locally Convex K | |
Vector Spaces | |
II.12 The Topological Vector Space C^an(M,E), part 2 | |
III.Lie Groups | |
III.13.Definitions and Foundations | |
III.14.The Universal Enveloping Algebra | |
III.15.The Concept of Free | |
ISBN: | 9783642211478 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v344 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups |
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Call number: | SPRINGER-2011-9783642183997:ONLINE Show nearby items on shelf |
Title: | Homogeneous Spaces and Equivariant Embeddings [electronic resource] |
Author(s): |
D.A Timashev |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standardreasons of algebraic geomet ry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally,open embeddings of a given homogeneous space. S uch equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of combinatorial nature (the Luna-Vusttheory) and description of various geometric and representation-theoretic prop erties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest inthe scope of this book. Spherical varieties include many classical examples, such as Grassmannians , flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the importantissues, including the recent substantial progress obtained in and around the theory of spherical varieties |
Note: | Springer eBooks |
Contents: | Introduction |
1 Algebraic Homogeneous Spaces | |
2 Complexity and Rank | |
3 General Theory of Embeddings | |
4 Invariant Valuations | |
5 Spherical Varieties | |
Appendices | |
Bibliography | |
Indices | |
ISBN: | 9783642183997 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v138 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups |
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Call number: | SPRINGER-2011-9783642156274:ONLINE Show nearby items on shelf |
Title: | Points and Lines [electronic resource] : Characterizing the Classical Geometries |
Author(s): |
Ernest Shult |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphicimages of them) are c haracterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups.These tools could be useful in shortening t he enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of aLie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appealto outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such acourse, or to elicit new research directions |
Note: | Springer eBooks |
Contents: | I.Basics |
1 Basics about Graphs | |
2 .Geometries: Basic Concepts | |
3 .Point | |
line Geometries | |
4.Hyperplanes, Embeddings and Teirlinck's Eheory | |
II.The Classical Geometries | |
5 .Projective Planes | |
6.Projective Spaces | |
7.Polar Spaces | |
8.Near Polygons | |
III.Methodology | |
9.Chamber Systems and Buildings | |
10.2 | |
Covers of Chamber Systems | |
11.Locally Truncated Diagram Geometries | |
12.Separated Systems of Singular Spaces | |
13 Cooperstein's Theory of Symplecta and Parapolar Spaces | |
IV.Applications to Other Lie Incidence Geometries | |
15.Characterizing the Classical Strong Parapolar Spac | |
ISBN: | 9783642156274 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Geometry |
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Call number: | SPRINGER-2011-9783642147005:ONLINE Show nearby items on shelf |
Title: | Topology and Geometry for Physics [electronic resource] |
Author(s): |
Helmut Eschrig |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts aresystematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points,as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physicsand gravitation |
Note: | Springer eBooks |
Contents: | Introduction |
Topology | |
Manifolds | |
Tensor Fields | |
Integration, Homology and Cohomology | |
Lie Groups | |
Bundles and Connections | |
Parallelism, Holonomy, Homotopy and (Co)homology | |
Riemannian Geometry | |
Compendium | |
ISBN: | 9783642147005 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, Volume 822, 0075-8450 : v822 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical physics |
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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-2011-9783642109379:ONLINE Show nearby items on shelf |
Title: | Gruppi, anelli di Lie e teoria della coomologia [electronic resource] |
Author(s): |
G Zappa |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | R. Baer: Complementation in finite gropus.- M. Lazard: Groupes, anneaux de Lie et problme de Burnside.- J. Tits: Sur les groupes algbriques afffines. Thormes fondamentaux de structure. Classification des groupessemisimples et gomtries associes |
Note: | Springer eBooks |
Contents: | R. Baer: Complementation in finite gropus |
M. Lazard: Groupes, anneaux de Lie et problme de Burnside | |
J. Tits: Sur les groupes algbriques afffines. Thormes fondamentaux de structure. Classification des groupes semisimples et gomtries associes | |
ISBN: | 9783642109379 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v20 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Topological Groups |
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Call number: | SPRINGER-2011-9781441974006:ONLINE Show nearby items on shelf |
Title: | An Introduction to Manifolds [electronic resource] |
Author(s): |
Loring W Tu |
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: | Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity , and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to comput e, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for aone-semester graduate or advanced undergraduate course, as well as by students engaged in sel f-study. The requisite point-set topology is included in an appendix of twenty-five pages other appendices review facts from real analysisand linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal un dergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for the author'spublication with Raoul Bott, Differential Forms in Algebraic Topology. |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface to the First Edition | |
Chapter 1. Euclidean Spaces | |
Chapter 2. Manifolds | |
Chapter 3. The Tangent Space | |
Chapter 4. Lie Groups and Lie Algebras | |
Chapter 5. Differential Forms | |
Chapter 6. Integration | |
Chapter 7. De Rham Theory | |
Appendices | |
A. Point | |
Set Topology | |
B. The Inverse Function Theorem on R(N) and Related Results | |
C. Existence of a Partition of Unity in General | |
D. Linear Algebra | |
E. Quaternions and the Symplectic Group | |
Solutions to Selected Exercises | |
Hints and Solutions to Selected End | |
of | |
Section Problems | |
List of Sym | |
ISBN: | 9781441974006 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2011-9781441972545:ONLINE Show nearby items on shelf |
Title: | Topology, Geometry and Gauge fields [electronic resource] : Foundations |
Author(s): |
Gregory L Naber |
Date: | 2011 |
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 is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The authors point of view is that the rekindled interest that mathematics andphysics have shown in ea ch other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and thetopological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementarypronouncements of quantum mechanics, and a solid background in real analy sis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topologicalspace and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 w ith instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outliningDonaldsons beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: It is unusual to find a book so carefully tailoredto the needs of this interdisciplinary area of mathematical physicsNaber combines a deep knowledge of his subject with an excellent informal writi ng style. (NZMS Newsletter) ...this book should be very interesting formathematicians and physicists (as well as other scientists) who are concerned with gauge theories. (ZENTRALBLATT FUER MATHEMATIK) The book is well written and the examples do a great s ervice to the reader. It will be a helpfulcompanion to anyone teaching or studying gauge theory (Mathematical Reviews) |
Note: | Springer eBooks |
Contents: | Contents: Preface |
Physical and geometrical motivation 1 Topological spaces | |
Homotopy groups | |
Principal bundles | |
Differentiable manifolds and matrix Lie groups | |
Gauge fields and Instantons. Appendix. References. Index | |
ISBN: | 9781441972545 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Applied Mathematics, 0939-2475 : v25 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry , Topology , Quantum theory |
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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-2011-9780857291608:ONLINE Show nearby items on shelf |
Title: | Representation Theory of the Virasoro Algebra [electronic resource] |
Author(s): |
Kenji Iohara Yoshiyuki Koga |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of theVirasoro algebra in a self- contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebrasassociated to the so-called minimal series represe ntations. Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. Fundamental resultsareorganizedin a unified way and existing proofs refined. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widelybelieved to be true, are collated, and results which are known but not verified are proven, such as the corrected s tructure theorem of Fock modules in chapter eight. This book will be of interest to a wide range of mathematicians andphysicists from the level of graduate students to researchers |
Note: | Springer eBooks |
Contents: | Preliminary |
Classification of Harish | |
Chandra Modules | |
The Jantzen Filtration | |
Determinant Formulae | |
Verma Modules I: Preliminaries | |
Verma Modules II: Structure Theorem | |
A Duality among Verma Modules | |
Fock Modules | |
Rational Vertex Operator Algebras | |
Coset Constructions for sl2 | |
Unitarisable Harish | |
Chandra Modules | |
Homological Algebras | |
Lie p | |
algebras | |
Vertex Operator Algebras | |
ISBN: | 9780857291608 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functions, special , Combinatorics |
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Call number: | SPRINGER-2011-9780857290212:ONLINE Show nearby items on shelf |
Title: | Ergodic Theory [electronic resource] : with a view towards Number Theory |
Author(s): |
Manfred Einsiedler Thomas Ward |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describesome recent application s to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between thecontinued fraction map and the modular surface , and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory andfunctional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory,homogenous dynamics or number theory |
Note: | Springer eBooks |
Contents: | Motivation |
Ergodicity, Recurrence and Mixing | |
Continued Fractions | |
Invariant Measures for Continuous Maps | |
Conditional Measures and Algebras | |
Factors and Joinings | |
Furstenbergs Proof of Szemeredis Theorem | |
Actions of Locally Compact Groups | |
Geodesic Flow on Quotients of the Hyperbolic Plane | |
Nilrotation | |
More Dynamics on Quotients of the Hyperbolic Plane | |
Appendix A: Measure Theory | |
Appendix B: Functional Analysis | |
Appendix C: Topological Groups | |
ISBN: | 9780857290212 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v259 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Number 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-2011-9780817647353:ONLINE Show nearby items on shelf |
Title: | Higher Structures in Geometry and Physics [electronic resource] : In Honor of Murray Gerstenhaber and Jim Stasheff |
Author(s): |
Alberto S Cattaneo Anthony Giaquinto Ping Xu |
Date: | 2011 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics such as algebra, algebraic topology, differentialgeometry, algebraic geome try, mathematical physics and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformationquantization, theory of algebroids and groupoids, symplec tic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role inrecent mathematical advances. For example, algebraic versions of higher homotopi es have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations anddeformation philosophy, a basic observation is that higher homotopy structures behave much better than st rict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometryand Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto,S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble |
Note: | Springer eBooks |
Contents: | Topics in Algebraic deformation theory |
Origins and breadth of the theory of higher homotopies | |
The deformation philosophy, quantization and noncommutative space | |
time structures | |
Differential geometry of Gerbes and differential forms | |
Symplectic connections of Ricci type and star products | |
Effective BatalinVilkovisky theories, equivariant configuration spaces and cyclic chains | |
Noncommutative calculus and the Gauss | |
Manin connection | |
The Lie algebra perturbation lemma | |
Twisting Elements in Homotopy G | |
algebras | |
Homological perturbation theory and homological mirror symmetry | |
ISBN: | 9780817647353 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v287 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics |
Author(s): |
Michael Ruzhansky Ville Turunen |
Date: | 2010 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part I Foundations of Analysis | |
A Sets, Topology and Metrics | |
B Elementary Functional Analysis | |
C Measure Theory and Integration | |
D Algebras | |
Part II Commutative Symmetries | |
1 Fourier Analysis on Rn | |
2 Pseudo | |
differential Operators on Rn | |
3 Periodic and Discrete Analysis | |
4 Pseudo | |
differential Operators on Tn | |
5 Commutator Characterisation of Pseudo | |
differential Operators | |
Part III Representation Theory of Compact Groups | |
6 Groups | |
7 Topological Groups | |
8 Linear Lie Groups | |
9 Hopf Algebras | |
Part IV Non | |
commutative Symmetries | |
10 Pseu | |
ISBN: | 9783764385149 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Pseudo-Differential Operators, Theory and Applications : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Global analysis , Differential equations, partial |
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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-2010-9780817649388: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-2010-9780817649340:ONLINE Show nearby items on shelf |
Title: | Cohomological and Geometric Approaches to Rationality Problems [electronic resource] : New Perspectives |
Author(s): |
Fedor Bogomolov Yuri Tschinkel |
Date: | 2010 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, or geometrically, on the dimension of the variety. A major success in 19th century algebraicgeometry was a complete sol ution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. These advances have led to many interdisciplinary applications of algebraic geometry.This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality ofmoduli spaces of curves, and rational points on algebraic varieties. Th is volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems. I. Bauer C.Bhning F. Bogomolov F. Catanese I. Cheltsov N. Hoffmann S.-J. Hu M.-C. Kang L. Katzarkov B. Kuny avskii A. Kuznetsov J. Park T. Petrov Yu. G. Prokhorov A.V. Pukhlikov Yu. Tschinkel |
Note: | Springer eBooks |
Contents: | The Rationality of Certain Moduli Spaces of Curves of Genus 3 |
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo | |
Unramified Cohomology of Finite Groups of Lie Type | |
Sextic Double Solids | |
Moduli Stacks of Vector Bundles on Curves and the KingSchofield Rationality Proof | |
Noethers Problem for Some | |
Groups | |
Generalized Homological Mirror Symmetry and Rationality Questions | |
The Bogomolov Multiplier of Finite Simple Groups | |
Derived Categories of Cubic Fourfolds | |
Fields of Invariants of Finite Linear Groups | |
The Rationality Problem and Birational Rig | |
ISBN: | 9780817649340 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v282 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups |
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Call number: | SPRINGER-2010-9780817647179:ONLINE Show nearby items on shelf |
Title: | Introduction to Quantum Groups [electronic resource] |
Author(s): |
George Lusztig |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specializedat roots of 1 and yiel d new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of thetheory are provided with canonical bases h aving rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includesthe case of quantum affine enveloping algebras and, more generall y, the quantum analogs of the KacMoody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Liegroups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Si nce large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook.**************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represen ts a landmark in the mathematical literature. Bulletin of the London Mathematical Society Thisbook is an important contribution to the field and can be recommended especially to mathematicians working in the field. EMS Newsletter The present book gives a very efficient presentation of an important part of quantum grouptheory. It is a valuable contribution to the literature. Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard re ference book for the material presentedand anyone interested in the DrinfeldJimbo algebras will have to study it very carefully. ZAA [T]his book is much more than an 'introduction to q |
Note: | Springer eBooks |
Contents: | Preface |
Part I: The Drinfeld | |
Jimbo Algebra U | |
Part II: Geometric Realization of f | |
Part III: Kashiwaras Operators and Applications | |
Part IV: Canonical Basis of U | |
Part V: Change of Rings | |
Part VI: Braid Group Action | |
Index of Notation | |
Index of Terminology | |
ISBN: | 9780817647179 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Topological Groups , Quantum theory , Mathematical 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-2009-9789491216367:ONLINE Show nearby items on shelf |
Title: | Topics in Measure Theory and Real Analysis [electronic resource] |
Author(s): |
Alexander B Kharazishvili |
Date: | 2009 |
Publisher: | Paris : Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measureextension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methodsare presented for solving the above mentio ned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures onsolvable uncountable groups non-separable extensions of invariant mea sures are constructed by using their ergodic components absolutely non-measurable additive functionals are constructed for certain classes of measures thestructure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). Newresults and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory an d general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin andSierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric sp aces, and so on. Essential information on these topics is also included in the text(primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only al lows the book to be used as a monograph but also as a course oflectures for students whose interests lie in set theory, real analysis, measure theory and general topology |
Note: | Springer eBooks |
ISBN: | 9789491216367 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Atlantis Studies in Mathematics, 1875-7634 : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2009-9783540853329:ONLINE Show nearby items on shelf |
Title: | Generalized Lie Theory in Mathematics, Physics and Beyond [electronic resource] |
Author(s): |
Sergei Silvestrov Eugen Paal Viktor Abramov Alexander Stolin |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to theinterplay between severa l rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensionsof differential calculus and geometry, non-ass ociative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book will be a useful source ofinspiration for a broad spectrum of researchers and for research students , and includes contributions from several large research communities in modern mathematics and physics. This volume consists of 5 parts comprising 25 chapters,which were contributed by 32 researchers from 12 different countries. All contributions in the v olume have been refereed |
Note: | Springer eBooks |
Contents: | Non |
Associative and Non | |
Commutative Structures for Physics | |
Moufang Transformations and Noether Currents | |
Weakly Nonassociative Algebras, Riccati and KP Hierarchies | |
Applications of Transvectants | |
Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics | |
A Rewriting Approach to Graph Invariants | |
Non | |
Commutative Deformations, Quantization, Homological Methods, and Representations | |
Graded q | |
Differential Algebra Approach to q | |
Connection | |
On Generalized N | |
Complexes Coming from Twisted Derivations | |
Remarks on Quantizations, Words and R | |
Matrices | |
Conn | |
ISBN: | 9783540853329 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2009-9783540772637:ONLINE Show nearby items on shelf |
Title: | The Geometry of Infinite-Dimensional Groups [electronic resource] |
Author(s): |
Boris Khesin Robert Wendt |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. Whileinfinite-dimensional groups often exh ibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjointorbits to knot theory, from optimal mass transport to moduli sp aces of flat connections on surfaces. The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry,and Hamiltonian systems |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
I Preliminaries | |
II Infinite | |
dimensional Lie Groups: Their Geometry, Orbits and Dynamical Systems | |
III Applications of Groups: Topological and Holomorphic Gauge Theories | |
Appendices | |
A1 Root Systems | |
A2 Compact Lie Groups | |
A3 Krichever | |
Novikov Algebras | |
A4 Khler Structures on the Virasoro and Loop Group Coadjoint Orbits | |
A5 Metrics and Diameters of the Group of Hamiltonian Diffeomorphisms | |
A6 Semi | |
Direct Extensions of the Diffeomorphism Group and Gas Dynamics | |
A7 The Drinfeld | |
Sokolov Reduction | |
A8 Surjectivity of the Exponential Map on Pseudo | |
ISBN: | 9783540772637 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics : v51 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Global analysis , Mathematical physics , Thermodynamics |
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