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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-2016-9783319313382:ONLINE Show nearby items on shelf |
Title: | Essays in Mathematics and its Applications In Honor of Vladimir Arnold |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (22 p.) |
Note: | 10.1007/978-3-319-31338-2 |
Contents: | A new way to compute the Rodrigues coefficients of functions of the Lie groups of matrices (D. Andrica, O.L. Chender) -- Quasimodes in integrable systems and semi-classical limit (M. Baldo, F. Raciti) -- Manifolds which are complex and symplectic bu t not Kahler (G. Bazzoni, V. Munoz) -- Solvability of a non clamped frictional contact problem with adhesion (O. Chau, D. Goeleven, R. Oujja) -- The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence (A. Fortunati, S. Wi ggins) -- Iterative Methods for the Elastography Inverse Problem of Locating Tumors (B. Jadamba, A.A. Khan, F. Raciti, C. Tammer, B. Winkler) -- Transversality theory with applications to differential equations (D. Motreanu, V.V. Motreanu) -- Lattice-like subsets of Euclidean Jordan algebras (A.B. Nemeth, S.Z. Nemeth) -- Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’ theorem (W.G. Nowak) -- On the fixed points of a Hamiltonian diffeomorphism in presence of |
fundamental group (K. Ono, A. Pajitnov) -- Some Generalizations of Fixed Point Theorems on S-Metric Spaces (N.Y. Ozgur, N.A. Tas) -- Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces (C. Park, J.R. Lee, T.M. Rassias) -- The Maslov Ind ex in PDEs Geometry (A. Prastaro) -- On the infimum of certain functionals (B. Ricceri) -- The Algebra of Gyrogroups: Cayley Theorem, Lagrange Theorem, and Isomorphism Theorems (T. Suksumran) -- Mild continuity properties of relations and relators in rela tor spaces (A. Szaz, A. Zakaria) -- Contraction Maps in Pseudometric Structures (M. Turinici) -- Novel Tools to Determine Hyperbolic Triangle Centers (A.A. Ungar) | |
ISBN: | 9783319313382 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Algebraic topology , Complex manifolds , Mathematics , Dynamical Systems and Ergodic Theory , Algebraic Topology , Manifolds and Cell Complexes (incl. Diff.Topology) , Global Analysis and Analysis on Manifolds |
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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-2016-9783319270760:ONLINE Show nearby items on shelf |
Title: | Surfaces in Classical Geometries A Treatment by Moving Frames |
Author(s): |
Gary R Jensen |
Date: | 2016 |
Size: | 1 online resource (61 p.) |
Note: | 10.1007/978-3-319-27076-0 |
Contents: | 1. Introduction -- 2. Lie Groups -- 3. Theory of Moving Frames -- 4. Euclidean Geometry -- 5. Spherical Geometry -- 6. Hyperbolic Geometry -- 7. Complex Structure -- 8. Minimal Immersions in Euclidean Space -- 9. Isothermic Immersions -- 10. The Bo nnet Problem -- 11. CMC 1 Surfaces in H3 -- 12. Möbius Geometry -- 13. Complex Structure and Möbius Geometry -- 14. Isothermic Immersions in Möbius Space -- 15. Lie Sphere Geometry -- Solutions to Select Problems -- References -- Index |
ISBN: | 9783319270760 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Differential geometry , Mathematics , Differential Geometry , Convex and Discrete Geometry |
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Call number: | SPRINGER-2014-9788132218142:ONLINE Show nearby items on shelf |
Title: | Groups of Exceptional Type, Coxeter Groups and Related Geometries [electronic resource] |
Author(s): |
N.S. Narasimha Sastry |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the themeof the book. Some of th e articles provide the latest developments in the subject some provide an overview of the current status of some important problems in this area some survey an area highlighting the current developments andsome provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of thelatest developments or to consider some problems for investigation |
Contents: | Chapter 1. A classification of Curtis |
Tits amalgams | |
Chapter 2. The use of valuations for classifying point | |
line geometries | |
Chapter 3. An outline of polar spaces: basics and advances | |
Chapter 4. Embeddings of Line | |
grassmannians of Polar Spaces in Grassmann Varieties | |
Chapter 5. Generation of Lie Incidence Geometries: A Survey | |
Chapter 6. Witt | |
Type Theorems for Subspaces of Lie Geometries: A Survey | |
Chapter 7. Embeddings of cotriangular spaces | |
Chapter 8. Unipotent Overgroups in Simple Algebraic Groups | |
Chapter 9. The axes of a Majorana representation of A12 | |
Chapter 10. GIT | |
ISBN: | 9788132218142 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v82 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Geometry |
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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-2014-9784431548287:ONLINE Show nearby items on shelf |
Title: | Introduction to Supergravity [electronic resource] |
Author(s): |
Yoshiaki Tanii |
Date: | 2014 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravityprovides a low-energy effec tive theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties ofsuperstring theory such as D-branes and string duality . This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classicalLagrangians (or field equations) and symmetry properties of supergravities . Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. Oneof the main features of this book is its detailed discussion of these non-compact symmetries. Th e aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, thediscussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this bookinclude the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magneticduality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities |
ISBN: | 9784431548287 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematical Physics, 2197-1757 : v1 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical physics |
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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-2014-9783642310317:ONLINE Show nearby items on shelf |
Title: | Vladimir I. Arnold - Collected Works [electronic resource] : Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972 |
Author(s): |
Vladimir I Arnold Alexander B Givental Boris A Khesin Alexander N Varchenko Victor A Vassiliev Oleg Ya Viro |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. Thissecond volume of his Coll ected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry |
Contents: | 1 Variational principle for three |
dimensional steady | |
state flows of an ideal fluid | |
2 On the Riemann curvature of diffeomorphism groups | |
3 Sur la topologie des coulements stationnaires des fluides parfaits (in French) | |
4 Conditions for non | |
linear stability of stationary plane curvilinear flows of an ideal fluid | |
5 On the topology of three | |
dimensional steady flows of an ideal fluid | |
6 On an a priori estimate in the theory of hydrodynamical stability | |
7 On the differential geometry of infinite | |
dimensional Lie groups and its application to the hydrodynamics of perfect fluids | |
8 On | |
ISBN: | 9783642310317 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Vladimir I. Arnold - Collected Works : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Mathematical physics |
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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-2014-9783319046754:ONLINE Show nearby items on shelf |
Title: | Geometry and its Applications [electronic resource] |
Author(s): |
Vladimir Rovenski Pawe Walczak |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, andosculation the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work isbased on the second international workshop entitled Geom etry and Symbolic Computations, held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and itsapplications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometricmodeling using symbolic programs such as Maple and Mathematica, as well as presentation of new results. |
Contents: | Part I: Geometry |
The Ricci flow on some generalized Wallach spaces (N.A. Abiev, A. Arvanitoyeorgos, Y.G. Nikonorov, P. Siasos) | |
Gaussian mean curvature flow for submanifolds in space forms (A. Borisenko, V. Rovenski) | |
Cantor laminationsand exceptional minimal sets in codimension one foliations(G. Hector) | |
Integral formulas in foliations theory (K. Andrzejewski, P. Walczak, V. Rovenski) | |
On prescribing the mixed scalar curvature of a foliations (V. Rovenski, L. Zelenko) | |
The partial Ricci flow for foliations (V. Rovenski) | |
Osculation in general (P. Walczak) | |
On stability of | |
ISBN: | 9783319046754 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v72 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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Call number: | SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf |
Title: | Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource] |
Author(s): |
Mahir Can Zhenheng Li Benjamin Steinberg Qiang Wang |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids |
Contents: | On Algebraic Semi groups and Monoids (M. Brion) |
Algebraic Semi groups are Strongly | |
regular (M. Brion, L. E. Renner) | |
Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha) | |
Representations of Reductive Normal Algebraic Monoids (S. Doty) | |
On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma) | |
The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang) | |
Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao) | |
Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen) | |
The Endomorphisms Monoid of a | |
ISBN: | 9781493909384 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Fields Institute Communications, 1069-5265 : v71 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics |
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Call number: | SPRINGER-2014-9781461485353:ONLINE Show nearby items on shelf |
Title: | Coherent States, Wavelets, and Their Generalizations [electronic resource] |
Author(s): |
Syed Twareque Ali Jean-Pierre Antoine Jean-Pierre Gazeau |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) andvarious generalizations o f wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherentstates, wavelets, and some of their generaliz ations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take aclassical-like view of quantum states in physics. Starting from the standar d theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are squareintegrable over a homogeneous space a further step allows one to dispense with the group context altog ether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensionalwavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups,Gazeau-Klauder coherent states,coherent states forthe relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potentialapplications, from the quantum physicallyoriented,likethe quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research forgraduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research liter |
Contents: | Canonical Coherent States |
Positive Operator | |
Valued Measures and Frames | |
Some Group Theory | |
Hilbert Spaces | |
Square Integrable and Holomorphic Kernels | |
Covariant Coherent States | |
Coherent States from Square Integrable Representations | |
Some Examples and Generalizations | |
CS of General Semidirect Product Groups | |
CS of Product Groups | |
CS Quantizations and Probabilistic Aspects | |
Direct Wavelet Transforms | |
Multidimensional Wavelets | |
Wavelets Related to Other G Groups | |
The Discretization Problem | |
Frames Sampling and All That | |
ISBN: | 9781461485353 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Group theory , Quantum theory |
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Call number: | SPRINGER-2013-9789400753457: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 |
Availability: | Click here to see Library holdings or inquire at
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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-2013-9783642321993:ONLINE Show nearby items on shelf |
Title: | Noncommutative Iwasawa Main Conjectures over Totally Real Fields [electronic resource] : Mnster, April 2011 |
Author(s): |
John Coates Peter Schneider R Sujatha Otmar Venjakob |
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: | The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.Non-commutative Iwas awa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field,independently by Ritter and Weiss on the one ha nd, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developedin the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fu kaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered animportant idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with anidea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The appro ach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideasin this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of s ome of the main general themes underlying these developments. The present volume will be a valuableresource for researchers working in both Iwasawa theory and the theory of automorphic forms. |
Note: | Springer eBooks |
Contents: | Preface |
John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non | |
commutative main conjectures for totally real fields | |
R. Sujatha: Reductions of the main conjecture | |
Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present | |
Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde | |
Mahesh Kakde: Congruences between abelian p | |
adic zeta functions | |
Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach | |
Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory | |
ISBN: | 9783642321993 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Number theory |
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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-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783034805858: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-2012-9783642154829:ONLINE Show nearby items on shelf |
Title: | Symmetries and Group Theory in Particle Physics [electronic resource] : An Introduction to Space-Time and Internal Symmetries |
Author(s): |
Giovanni Costa Gianluigi Fogli |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is anintroduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of theMinkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standardmodel of particle physics. This book, based on several courses given by th e authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge ofclassical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures |
Note: | Springer eBooks |
Contents: | Introduction to Lie Groups and their Representations |
The Rotation Group | |
The Homogeneous Lorentz Group | |
The Poincare Transformation | |
One Particle and Two Particle States | |
Discrete Operations | |
Relativistic Equations | |
Unitary Symmetries | |
Gauge Symmetries | |
Rotation Matrices and Clebsch | |
Gordan Coeficients | |
Symmetric Goups and Identical Particles | |
Young Tableaux and Irreducible Representations ot he Unitary Groups | |
Solutions | |
Index | |
ISBN: | 9783642154829 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v823 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2012-9783034804202:ONLINE Show nearby items on shelf |
Title: | Classical Geometries in Modern Contexts [electronic resource] : Geometry of Real Inner Product Spaces Third Edition |
Author(s): |
Walter Benz |
Date: | 2012 |
Edition: | 3rd ed. 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolicgeometry with respect to nat ural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Mbius and Lie as well as geometries where Lorentz transformations play thekey role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentztransformations. A real benefit is the dimension-free approach to important geome trical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these samespaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz -Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result inthis edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the ge ometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all xin X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for read ing this book are basic linear algebra and basic 2- and 3-dimensional real geometry.This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in m odern and general contexts |
Note: | Springer eBooks |
Contents: | Preface |
1 Translation Groups | |
2 Euclidean and Hyperbolic Geometry | |
3 Sphere Geometries of Mbius and Lie | |
4 Lorentz Transformations | |
5 Projective Mappings, Isomorphism Theorems | |
6 Planes of Leibniz, Lines of Weierstrass, Varia | |
A Notation and symbols | |
B Bibliography | |
Index | |
ISBN: | 9783034804202 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry , Mathematical physics |
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Call number: | SPRINGER-2012-9781461442448:ONLINE Show nearby items on shelf |
Title: | Homogeneous Finsler Spaces [electronic resource] |
Author(s): |
Shaoqiang Deng |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is a unique addition to the existing literature in the field of Finsler geometry. This is the first monograph to deal exclusively with homogeneous Finsler geometry and to make serious use of Lie theory in the study ofthis rapidly developing field. The increasing activity in Finsler geometry can be attested in large part to the driving influence of S.S. Chern, its proven use in many fields of scientific study such as relativity, optics, geosciences,mathematical biology, and psychology, and i ts promising reach to real-world applications. This work has potential for broad readership it is a valuable resource not only for specialists of Finsler geometry, but also for differentialgeometers who are familiar with Lie theory, transformation groups, and homogeneous spaces. The exposition is rigorous, yet gently engages the readerstudent and researcher alikein developing a ground level understanding of thesubject. A one-term graduate course in differential geometry and elementary topology are prerequ isites. In order to enhance understanding, the author gives a detailed introduction and motivation for the topics of each chapter, as wellas historical aspects of the subject, numerous well-selected examples, and thoroughly proved main results. Comments f or potential further development are presented in Chapters 37. A basic introduction to Finsler geometry isincluded in Chapter 1 the essentials of the related classical theory of Lie groups, homogeneous spaces and groups of isometries are presented in Chap ters 23. Then the author develops the theory of homogeneous spaces within theFinslerian framework. Chapters 46 deal with homogeneous, symmetric and weakly symmetric Finsler spaces. Chapter 7 is entirely devoted to homogeneous Randers spaces, which are goo d candidates for real world applications andbeautiful illustrators of the developed theory |
Note: | Springer eBooks |
Contents: | Preface |
Acknowledgements | |
1. Introduction to Finsler Geometry | |
2. Lie Groups and Homogenous Spaces | |
3. The Group of Isometries | |
4. Homogeneous Finsler Spaces | |
5. Symmetric Finsler Spaces | |
6. Weakly Symmetric Finsler Spaces | |
7. Homogeneous Randers Spaces | |
References | |
Index. | |
ISBN: | 9781461442448 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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Call number: | SPRINGER-2012-9781461407096:ONLINE Show nearby items on shelf |
Title: | Buildings, Finite Geometries and Groups [electronic resource] : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010 |
Author(s): |
N.S. Narasimha Sastry |
Date: | 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on Buildings, Finite Geometries and Groups organized at the Indian Statistical Institute, Bangalore, from August 29 31,2010. These contributors include so me of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lietheory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on currentdevelopments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields |
Note: | Springer eBooks |
Contents: | 1. On Characterizing Designs By Their Codes (B. Bagchi) |
2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen) | |
3. Properties of a 27 | |
dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow) | |
4. On the Geometry of Global Function Fields, the Riemann | |
Roch Theorem, and Finiteness Properties of S | |
arithmetic Groups (R. Gramlich) | |
5. Some Remarks on Two | |
Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lbeck) | |
6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji) | |
7. On Isotypies Between Galois Conj | |
ISBN: | 9781461407096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics, 2190-5614 : v10 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9781447123538:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Signal and Image Analysis and Representation [electronic resource] |
Author(s): |
Luc Florack Remco Duits Geurt Jongbloed Marie-Colette Lieshout Laurie Davies |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living onan n-dimensional smo oth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. Incontrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed forthe sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interestedin the fundamental methodology per se. Covering many topics at the forefront of curre nt research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduatestudents and researchers in the fields of computer vision, medical imaging and visual perception |
Note: | Springer eBooks |
Contents: | A Short Introduction to Diffusion |
like Methods | |
Adaptive Filtering using Channel Representations | |
3D | |
Coherence | |
Enhancing Diffusion Filtering for Matrix Fields | |
Structural Adaptive Smoothing: Principles and Applications in Imaging | |
SPD Tensors Regularization via Iwasawa Decomposition | |
Sparse Representation of Video Data by Adaptive Tetrahedralizations | |
Continuous Diffusion Wavelet Transforms and Scale Space over Euclidean Spaces and Noncommutative Lie Groups | |
Left Invariant Evolution Equations on Gabor Transforms | |
Scale Space Representations Locally Adapted to the Geometry of Ba | |
ISBN: | 9781447123538 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Computational Imaging and Vision, 1381-6446 : v41 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision |
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Call number: | SPRINGER-2012-9781441999825:ONLINE Show nearby items on shelf |
Title: | Introduction to Smooth Manifolds [electronic resource] |
Author(s): |
John M Lee |
Date: | 2012 |
Edition: | 2nd ed. 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific researchsmoothstructures, tangent vector s and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. Theapproach is as concrete as possible, with pictu res and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Thissecond edition has been extensively revised and clarified, and the topic s have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, muchearlier so that they can be used throughout the book. A few new topics have been added, notably Sards theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study offirst-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds , and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, thefundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis |
Note: | Springer eBooks |
Contents: | Preface |
1 Smooth Manifolds | |
2 Smooth Maps | |
3 Tangent Vectors | |
4 Submersions, Immersions, and Embeddings | |
5 Submanifolds | |
6 Sard's Theorem | |
7 Lie Groups | |
8 Vector Fields | |
9 Integral Curves and Flows | |
10 Vector Bundles | |
11 The Cotangent Bundle | |
12 Tensors | |
13 Riemannian Metrics | |
14 Differential Forms | |
15 Orientations | |
16 Integration on Manifolds | |
17 De Rham Cohomology | |
18 The de Rham Theorem | |
19Distributions and Foliations | |
20 The Exponential Map | |
21 Quotient Manifolds | |
22 Symplectic Manifolds | |
Appendix A: Review of Topology | |
Appendix B: Review | |
ISBN: | 9781441999825 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v218 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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Call number: | SPRINGER-2012-9780817683344:ONLINE Show nearby items on shelf |
Title: | Multiple Dirichlet Series, L-functions and Automorphic Forms [electronic resource] |
Author(s): |
Daniel Bump Solomon Friedberg Dorian Goldfeld |
Date: | 2012 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibitssurprising and deep connection s to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together.The volume also includes papers on automorphic forms a nd L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representationtheory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D.Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. S uzuki, H. Tsumura |
Note: | Springer eBooks |
Contents: | Preface |
Introduction: Multiple Dirichlet Series | |
A Crystal Description for Symplectic Multiple Dirichlet Series | |
Metaplectic Whittaker Functions and Crystals of Type B | |
Metaplectic Ice | |
Littelmann patterns and Weyl Group Multiple Dirichlet Series of Type D | |
Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series | |
Natural Boundaries and Integral Moments of L | |
functions | |
A Trace Formula of Special Values of Automorphic L | |
functions | |
TheAdjoint L | |
function of SU(2,1) | |
Symplectic Ice | |
On Witten Multiple Zeta | |
Functions Associated with Semisimple Lie Algebr | |
ISBN: | 9780817683344 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v300 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Functions, special , Combinatorics , Number theory |
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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-2011-9783642212987:ONLINE Show nearby items on shelf |
Title: | Riemannian Geometry and Geometric Analysis [electronic resource] |
Author(s): |
Jrgen Jost |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that hadfound a spectacular su ccess in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound newideas and methods in geometry. The 6th edit ion includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of thebook. From the reviews: This book provides a very readable intro duction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is mostwelcome. Mathematical Reviews ...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section Perspectives, written with the aim to place the material in a broadercontext and explain further results and directions. Zentralblatt MATH |
Note: | Springer eBooks |
Contents: | 1. Riemannian Manifolds |
2. Lie Groups and Vector Bundles | |
3. The Laplace Operator and Harmonic Differential Forms | |
4. Connections and Curvature | |
5. Geodesics and Jacobi Fields | |
6. Symmetric Spaces and Kahler Manifolds | |
7. Morse Theory and Floer Homology | |
8. Harmonic Maps between Riemannian Manifolds | |
9. Harmonic Maps from Riemann Surfaces | |
10. Variational Problems from Quantum Field Theory | |
A. Linear Elliptic Partial Differential Equations | |
A.1 Sobolev Spaces | |
A.2 Linear Elliptic Equations | |
A.3 Linear Parabolic Equations | |
B. Fundamental Groups and Covering Spaces | |
ISBN: | 9783642212987 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry |
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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-2011-9783642111174:ONLINE Show nearby items on shelf |
Title: | Harmonic Analysis and Group Representation [electronic resource] |
Author(s): |
A. Fig Talamanca |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lectures: A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties.- M Cowling: Unitary and uniformly bounded representations of some simple Lie groups.- M. Duflo: Construction de representations unitaires dun groupede Lie.- R. Howe: On a no tion of rank for unitary representations of the classical groups.- V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups.- R. Zimmer: Ergodic theory, group representations and rigidity.- Seminars:A. Koranyi: Some applications of Gelfand pair s in classical analysis |
Note: | Springer eBooks |
Contents: | A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties |
M Cowling: Unitary and uniformly bounded representations of some simple Lie groups | |
M. Duflo: Construction de reprsentations unitaires dun groupe de Lie | |
R. Howe: On a notion of rank for unitary representations of the classical groups | |
A. Koranyi: Some applications of Gelfand pairs in classical analysis | |
V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups | |
R. Zimmer: Ergodic theory, group representations and rigidity | |
ISBN: | 9783642111174 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v82 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Number theory |
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