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SPIRES-BOOKS: FIND KEYWORD TOPOLOGICAL GROUPS,LIE GROUPS *END*INIT* use /tmp/qspiwww.webspi1/17284.9 QRY 131.225.70.96 . find keyword topological groups,lie groups ( in books using www Cover
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Call number:9783319297347:ONLINE Show nearby items on shelf
Title:Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories
Author(s): Eckehard W Mielke
Date:2017
Edition:2nd ed. 2017
Size:1 online resource (XVII, 373 p. 18 illus., 8 illus. in color p.)
Contents:Preface -- 1 Historical background -- 2 Geometry of gauge fields -- 3 Maxwell and Yang-Mills theory -- 4 Gravitation as a gauge theory -- 5 Einstein-Cartan theory -- 6 Teleparallelism -- 7 Yang’s theory of gravity -- 8 BRST
quantization of gravity -- 9 Gravitational instantons -- 10 Three-dimensional gravity -- 11 Spinor bundles -- 12 Chiral anomalies -- 13 Topological SL(5R) gauge invariant action -- 14 Geometrodynamics and its extensions -- 15 Color
Geometrodynamics -- 16 Geometrodynamical model of quark confinement?- Appendix A Notation and mathematical terms -- Appendix B Calculus of exterior forms -- Appendix C Lie groups
ISBN:9783319297347
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Mathematical physics , Gravitation , Elementary particles (Physics) , Quantum field theory , Physics , Classical and Quantum Gravitation, Relativity Theory , Mathematical Physics , Elementary Particles, Quantum Field Theory
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Call number:SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf
Title:Manifolds, Sheaves, and Cohomology
Author(s): Torsten Wedhorn
Date:2016
Size:1 online resource (354 p.)
Note:10.1007/978-3-658-10633-1
Contents:Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis
ISBN:9783658106331
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds
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Call number:SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf
Title:Extensions of Positive Definite Functions Applications and Their Harmonic Analysis
Author(s): Palle Jorgensen
Date:2016
Size:1 online resource (9 p.)
Note:10.1007/978-3-319-39780-1
ISBN:9783319397801
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2160
Keywords: Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes
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Call number:SPRINGER-2016-9783319392868:ONLINE Show nearby items on shelf
Title:Operator Algebras and Applications The Abel Symposium 2015
Author(s):
Date:2016
Size:1 online resource (2 p.)
Note:10.1007/978-3-319-39286-8
Contents:C*-tensor categories and subfactors for totally disconnected groups: Y. Arano and S. Vaes -- Decomposable approximations revisited: N.P. Brown, J.R. Carrión and S. White -- Exotic crossed products: A. Buss, S. Echterhoff, and R. Willett -- On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra: T. M. Carlsen and A. Sims -- Commutator inequalities via Schur products: E. Christensen -- C*-algebras associated with algebraic actions: J. Cuntz -- A new look at C*-simplicit y and the unique trace property of a group: U. Haagerup -- Equilibrium states on graph algebras: A. an Huef and I. Raeburn -- Semigroup C_-algebras: X. Li -- Topological full groups of étale groupoids: H. Matui -- Towards a classification of compact quan tum groups of Lie type: S. Neshveyev and M. Yamashita -- A homology theory for Smale spaces: a summary: I.F. Putnam -- On the positive eigenvalues and eigenvectors of a non-negative matrix: K. Thomsen -- Classification of graph algebras: a
selective survey: M. Tomforde -- QDQ vs. UCT: W. Winter
ISBN:9783319392868
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Abel Symposia: 12
Keywords: Mathematics , K-theory , Dynamics , Ergodic theory , Functional analysis , Mathematical physics , Mathematics , Functional Analysis , Dynamical Systems and Ergodic Theory , K-Theory , Mathematical Physics
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Call number:SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf
Title:Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014
Author(s):
Date:2016
Edition:1st ed. 2016
Size:1 online resource (332 p.)
Note:10.1007/978-3-319-30451-9
ISBN:9783319304519
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 159
Keywords: Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups
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Call number:SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf
Title:Quantization on Nilpotent Lie Groups
Author(s): Veronique Fischer
Date:2016
Edition:1st ed. 2016
Size:1 online resource (557 p.)
Note:10.1007/978-3-319-29558-9
Contents:Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index
ISBN:9783319295589
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 314
Keywords: Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics
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Call number:SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf
Title:Basic Modern Algebra with Applications [electronic resource]
Author(s): Mahima Ranjan Adhikari
Avishek Adhikari
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource
Contents:Prerequisites: Basics of Set Theory and Integers
Groups: Introductory Concepts
Actions of Groups, Topological Groups and semigroups
Rings: Introductory Concepts
Ideals of Rings: Introductory concepts
Factorization in Integral Domains and in Polynomial Rings
Rings with Chain Conditions
Vector Spaces
Modules
Algebraic Aspects of Number Theory
Algebraic Numbers
Introduction to Mathematical Cryptography
Appendix A: Some Aspects of Semirings
Appendix B: Category Theory
Appendix C: A Brief Historical Note
ISBN:9788132215998
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Number theory
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Call number:SPRINGER-2014-9783642553615:ONLINE Show nearby items on shelf
Title:Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011
Author(s): Abdenacer Makhlouf
Eugen Paal
Sergei D Silvestrov
Alexander Stolin
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students
Contents:Part I Algebra
Part II Geometry
Part III Dynamical Symmetries and Conservation Laws
Part IV Mathematical Physics and Applications
ISBN:9783642553615
Series:eBooks
Series:SpringerLink
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics
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Call number:SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf
Title:Probability on Compact Lie Groups [electronic resource]
Author(s): David Applebaum
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects
Contents:Introduction
1.Lie Groups
2.Representations, Peter
Weyl Theory and Weights
3.Analysis on Compact Lie Groups
4.Probability Measures on Compact Lie Groups
5.Convolution Semigroups of Measures
6.Deconvolution Density Estimation
Appendices
Index
Bibliography
ISBN:9783319078427
Series:eBooks
Series:SpringerLink
Series:Probability Theory and Stochastic Modelling, 2199-3130 : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory)
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Call number:SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf
Title:Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource]
Author(s): Mahir Can
Zhenheng Li
Benjamin Steinberg
Qiang Wang
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids
Contents:On Algebraic Semi groups and Monoids (M. Brion)
Algebraic Semi groups are Strongly
regular (M. Brion, L. E. Renner)
Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha)
Representations of Reductive Normal Algebraic Monoids (S. Doty)
On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma)
The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang)
Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao)
Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen)
The Endomorphisms Monoid of a
ISBN:9781493909384
Series:eBooks
Series:SpringerLink
Series:Fields Institute Communications, 1069-5265 : v71
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics
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Call number:SPRINGER-2013-9789400753457:ONLINE Show nearby items on shelf
Title:Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems
Author(s): Gerd Rudolph
Matthias Schmidt
Date:2013
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact
Note:Springer eBooks
Contents:1 Differentiable manifolds
2 Vector bundles
3 Vector fields
4 Differential forms
5 Lie groups
6 Lie group actions
7 Linear symplectic algebra
8 Symplectic geometry
9 Hamiltonian systems
10 Symmetries
11 Integrability
12 Hamilton
Jacobi theory
References
ISBN:9789400753457
Series:e-books
Series:SpringerLink (Online service)
Series:Theoretical and Mathematical Physics, 1864-5879
Series:Physics and Astronomy (Springer-11651)
Keywords: Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics
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Call number:SPRINGER-2013-9784431542704:ONLINE Show nearby items on shelf
Title:Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop
Author(s): Vladimir Dobrev
Date:2013
Publisher:Tokyo : Springer Japan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to asystem yields in general so me notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantumgroups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples ofthese new trends are presented in this volume, based on contributions fr om the Workshop Lie Theory and Its Applications in Physics held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience ofmathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theo ry
Note:Springer eBooks
ISBN:9784431542704
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v36
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Geometry
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Call number:SPRINGER-2013-9783642362163:ONLINE Show nearby items on shelf
Title:Clifford Algebras and Lie Theory [electronic resource]
Author(s): Eckhard Meinrenken
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results onsymmetric bilinear form s and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes apresentation of Petraccis proof of the PoincarBirk hoffWitt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lietheory include Duflos theorem for the case of quadratic Lie algebras, multiplets of rep resentations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over asemisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fa scinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principalsl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Cliffor d theory, relevant for students and researchers in mathematics andphysics
Note:Springer eBooks
Contents:Preface
Conventions
List of Symbols
1 Symmetric bilinear forms
2 Clifford algebras
3 The spin representation
4 Covariant and contravariant spinors
5 Enveloping algebras
6 Weil algebras
7 Quantum Weil algebras
8 Applications to reductive Lie algebras
9 D(g k) as a geometric Dirac operator
10 The HopfKoszulSamelson Theorem
11 The Clifford algebra of a reductive Lie algebra
A Graded and filtered super spaces
B Reductive Lie algebras
C Background on Lie groups
References
Index
ISBN:9783642362163
Series:e-books
Series:SpringerLink (Online service)
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v58
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Mathematical physics
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Call number:SPRINGER-2013-9783642310904:ONLINE Show nearby items on shelf
Title:Poisson Structures [electronic resource]
Author(s): Camille Laurent-Gengoux
Anne Pichereau
Pol Vanhaecke
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures
Note:Springer eBooks
Contents:Part I Theoretical Background:1.Poisson Structures: Basic Definitions
2.Poisson Structures: Basic Constructions
3.Multi
Derivations and Khler Forms
4.Poisson (Co)Homology
5.Reduction
Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds
7.Linear Poisson Structures and Lie Algebras
8.Higher Degree Poisson Structures
9.Poisson Structures in Dimensions Two and Three
10.R
Brackets and r
Brackets
11.PoissonLie Groups
Part III Applications:12.Liouville Integrable Systems
13.Deformation Quantization
A Multilinear Algebra
B Real
ISBN:9783642310904
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry
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Call number:SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource]
Author(s): Shahla Molahajloo
Stevan Pilipovi
Joachim Toft
M. W Wong
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series
Note:Springer eBooks
Contents:Preface
Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds
The Singular Functions of Branching Edge Asymptotics
The Heat Kernel and Green Function of the Sub
Laplacian on the Heisenberg Group
Metaplectic Equivalence of the Hierarchical Twisted Laplacian
The Heat Kernel and Green Function of a Sub
Laplacian on the Hierarchical Heisenberg Group
Lp
Bounds for Pseudo
Differential Operators on the Torus
Multiplication Properties in Gelfand
Shilov Pseudo
Differential Calculus
Operator Invariance
Initial Value Problems in the Time
Frequency Do
ISBN:9783034805858
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v231
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial
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Call number:SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf
Title:Lie Groups [electronic resource]
Author(s): Daniel Bump
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations
Note:Springer eBooks
Contents:Part I: Compact Topological Groups
1 Haar Measure
2 Schur Orthogonality
3 Compact Operators
4 The PeterWeyl Theorem
Part II: Compact Lie Groups
5 Lie Subgroups of GL(n,C)
6 Vector Fields
7 Left
Invariant Vector Fields
8 The Exponential Map
9 Tensors and Universal Properties
10 The Universal Enveloping Algebra
11 Extension of Scalars
12 Representations of sl(2,C)
13 The Universal Cover
14 The Local Frobenius Theorem
15 Tori
16 Geodesics and Maximal Tori
17 The Weyl Integration Formula
18 The Root System
19 Examples of Root Systems
ISBN:9781461480242
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v225
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
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Call number:SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf
Title:Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday
Author(s): Alan Huckleberry
Ivan Penkov
Gregg Zuckerman
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted
Note:Springer eBooks
Contents:Preface
Real group orbits on flag manifolds
Complex connections with trivial holonomy
Indefinite harmonic theory and harmonic spinors
Twistor theory and the harmonic hull
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets
Propagation of the multiplicity
freeness property for holomorphic vector bundles
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf
Weakly harmonic Maa forms and the princi
ISBN:9781461471936
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v306
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Functional analysis
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Call number:SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf
Title:New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number
Author(s): Garret Sobczyk
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s
Note:Springer eBooks
Contents:1 Modular Number Systems
2 Complex and Hyperbolic Numbers
3 Geometric Algebra
4 Vector Spaces and Matrices
5 Outer Product and Determinants
6 Systems of Linear Equations
7 Linear Transformations on R^n
8 Structure of a Linear Operator
9 Linear and Bilinear Forms
10 Hermitian Inner Product Spaces
11 Geometry of Moving Planes
12 Representations of the Symmetric Group
13 Calculus on m
Surfaces
14 Differential Geometry of Curves
15 Differential Geometry of k
Surfaces
16 Mappings Between Surfaces
17 Non
Euclidean and Projective Geometries
18 Lie Gr
ISBN:9780817683856
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2013-9780817683641:ONLINE Show nearby items on shelf
Title:Configurations from a Graphical Viewpoint [electronic resource]
Author(s): Toma Pisanski
Brigitte Servatius
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. Inthis self-contained tex tbook, algebraic graph theory is used to introduce groups topological graph theory is used to explore surfaces and geometric graph theory is implemented to analyze incidence geometries. After a preview ofconfigurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied.Geometric aspects, some historical remarks, references, and applicationsof classicalconfigurationsappear in the last chapter. With over two hundred illustrations, challenging exercises at t he end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint iswell suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicia ns and researchers
Note:Springer eBooks
Contents:Preface
Introduction
Graphs
Groups, Actions, and Symmetry
Maps
Combinatorial Configurations
Geometric Configurations
Index
Bibliography
ISBN:9780817683641
Series:e-books
Series:SpringerLink (Online service)
Series:Birkhuser Advanced Texts Basler Lehrbcher
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Combinatorics , Geometry , Topology
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Call number:SPRINGER-2012-9783642227172:ONLINE Show nearby items on shelf
Title:The Schrdinger-Virasoro Algebra [electronic resource] Mathematical structure and dynamical Schrdinger symmetries
Author(s): Jrmie Unterberger
Claude Roger
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schrdinger-Virasoro algebra. Just as Poincar invariance or conformal (Virasoro) invarianceplay a key role in understanding , respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study ofsome models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Liealgebra touches upon topics as various as statistical physics, vertex algebras, Po isson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and thespectral theory of Schrdinger operators.
Note:Springer eBooks
Contents:Introduction
Geometric Definitions of SV
Basic Algebraic and Geometric Features
Coadjoint Representaion
Induced Representations and Verma Modules
Coinduced Representations
Vertex Representations
Cohomology, Extensions and Deformations
Action of sv on Schrdinger and Dirac Operators
Monodromy of Schrdinger Operators
Poisson Structures and Schrdinger Operators
Supersymmetric Extensions of sv
Appendix to chapter 6
Appendix to chapter 11
Index
ISBN:9783642227172
Series:e-books
Series:SpringerLink (Online service)
Series:Theoretical and Mathematical Physics, 1864-5879
Series:Physics and Astronomy (Springer-11651)
Keywords: Algebra , Topological Groups , Mathematical physics
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Call number:SPRINGER-2012-9783642227165:ONLINE Show nearby items on shelf
Title:The Schringer-Virasoro Algebra [electronic resource]
Author(s): Jie Unterberger
Claude Roger
Date:2012
Publisher:Springer Berlin Heidelberg
Size:1 online resource
Note:Monograph
Note:Springer 2012 Physics and Astronomy eBook collection
Note:Springer e-book platform
ISBN:9783642227165
Series:Texts and Monographs in Physics
Series:e-books
Keywords: Mathematical Methods in Physics , Topological Groups, Lie Groups , Mathematical Physics , Category Theory, Homological Algebra , Statistical Physics, Dynamical Systems and Complexity
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Call number:SPRINGER-2012-9783642225970:ONLINE Show nearby items on shelf
Title:Topics in Noncommutative Algebra [electronic resource] : The Theorem of Campbell, Baker, Hausdorff and Dynkin
Author(s): Andrea Bonfiglioli
Roberta Fulci
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, NumericalAnalysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra ornot) to understand and apply the statements and numero us corollaries of the main result 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view andnotation 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincar, Pascal, Campbell, Baker, Hausdorff and Dynkin 4) give an outlook on theapplications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) 5 ) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modernliterature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems an d applications. The book assumes some undergraduate-level knowledge of algebra and analysis,but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool fo r beginners in Algebra
Note:Springer eBooks
Contents:1 Historical Overview
Part I Algebraic Proofs of the CBHD Theorem
2 Background Algebra
3 The Main Proof of the CBHD Theorem
4 Some Short Proofs of the CBHD Theorem
5 Convergence and Associativity for the CBHD Theorem
6 CBHD, PBW and the Free Lie Algebras
Part II Proofs of the Algebraic Prerequisites
7 Proofs of the Algebraic Prerequisites
8 Construction of Free Lie Algebras
9 Formal Power Series in One Indeterminate
10 Symmetric Algebra
ISBN:9783642225970
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2034
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry
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Call number:SPRINGER-2012-9780817682743:ONLINE Show nearby items on shelf
Title:Highlights in Lie Algebraic Methods [electronic resource]
Author(s): Anthony Joseph
Anna Melnikov
Ivan Penkov
Date:2012
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:An outgrowth of a two-week summer sessionat Jacobs University inBremen, Germany in August 2009 (Structures in Lie Theory, Crystals, Derived Functors, HarishChandra Modules, Invariants and Quivers), this volume consistsof expository and research artic les that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and KacMoody Lie algebras, modularrepresentations, primitive ideals, representation theory of Arti n algebras and quivers, KacMoody superalgebras, categories of HarishChandra modules, cohomological methods, and cluster algebras. List of Contributors: M. BoosM. Brion J. Fuchs M. Gorelik A. Joseph M. Reineke C. Schweigert V. Serganova A. Seven W. Soergel B. Wilson G. Zuckerman
Note:Springer eBooks
Contents:Preface
Part I: The Courses
1 Spherical Varieties
2 Consequences of the Littelmann Path Model for the Structure of the Kashiwara B() Crystal
3 Structure and Representation Theory of KacMoody Superalgebras
4 Categories of HarishChandra Modules
5 Generalized HarishChandra Modules
Part II: The Papers
6 B
Orbits of 2
Nilpotent Matrices
7 The Weyl Denominator Identity for Finite
Dimensional Lie Superalgebras
8 Hopf Algebras and Frobenius Algebras in Finite Tensor Categories
9 Mutation Classes of 3 x 3 Generalized Cartan Matrices
10 Contractions and Po
ISBN:9780817682743
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v295
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Matrix theory , Topological Groups
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Call number:SPRINGER-2012-9780817682712:ONLINE Show nearby items on shelf
Title:Differentiable Manifolds [electronic resource] : A Theoretical Physics Approach
Author(s): Gerardo F Torres del Castillo
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The works first three chaptersintroduce the basic concep ts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequentlyemployed in the study of differential equations ( Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked outin detail, as well as exercises intended to show how the formalism is a pplied to actual computations and to emphasize the connections among various areas of mathematics. Differentiable Manifolds is addressed to advanced undergraduateor beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics
Note:Springer eBooks
Contents:Preface
1 Manifolds
2 Lie Derivatives
3 Differential Forms
4 Integral Manifolds
5 Connections
6. Riemannian Manifolds
7 Lie Groups
8 Hamiltonian Classical Mechanics
References
Index
ISBN:9780817682712
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Cell aggregation Mathematics , Mathematical physics , Mechanics
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Call number:SPRINGER-2012-9780817649449:ONLINE Show nearby items on shelf
Title:Stochastic Models, Information Theory, and Lie Groups, Volume 2 [electronic resource] : Analytic Methods and Modern Applications
Author(s): Gregory S Chirikjian
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges betweenfields that are rarely stu died by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, andgroup-theoretic concepts in the modeling of physical p henomena. Volume 1 establishes the geometric and statistical foundations required to understand the fundamentals of continuous-time stochastic processes, differential geometry, andthe probabilistic foundations of information theory. Volume 2 delves deeper into relationships between these topics, including stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statisticalanalysis, and error propagation on Lie groups. Key features and topics of Volume 2: * The author reviews the concept ofandfunctions and integration onLie groups with many concrete examples. * Extensive exercises andmotivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes on Lie groups or geometric aspects of probability and statistics. *Specific application areas are explored,including biomolecular statistical mechanics and information-driven motion in robotics. * The concrete presentation style makes it easy for readers to obtain numeri cal solutions for their own problems the emphasis is on how tocalculate quantities rather than how to prove theorems. * Modern problems at the interface of mechanics, control theory, and communications are handled in a unified framework and multiple direc tions for future research are explored.Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practition
Note:Springer eBooks
Contents:Lie Groups I: Introduction and Examples
Lie Groups II: Differential Geometric Properties
Lie Groups III: Integration, Convolution, and Fourier Analysis
Variational Calculus on Lie Groups
Statistical Mechanics and Ergodic Theory
Parts Entropy and the Principal Kinematic Formula
Estimation and Multivariate Analysis in R^n
Information, Communication, and Group Therapy
Algebraic and Geometric Coding Theory
Information Theory on Lie Groups
Stochastic Processes on Lie Groups
Locomotion and Perception as Communication over Principal Fiber Bundles and A Survey of Addi
ISBN:9780817649449
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global differential geometry , Distribution (Probability theory) , Mathematical physics , Engineering mathematics
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Call number:SPRINGER-2012-9780817648176:ONLINE Show nearby items on shelf
Title:Representation Theory, Complex Analysis, and Integral Geometry [electronic resource]
Author(s): Bernhard Krtz
Omer Offen
Eitan Sayag
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is an outgrowth of the special term Harmonic Analysis, Representation Theory, and Integral Geometry, held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonnduring the summer of 2007. The contributions in the volume provide a window into a variety of subjects related to reductive groups: real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, geometry offlag varieties, restriction theory of representations, modern aspects of special functions, multiple Dirichlet series, and unfolding identities in the theory of automorphic forms. Throughout the work, great emphasis was placed onmaking the articles accessible to interested newcomers to these fields and gradu ate students. Representation Theory, Complex Analysis, and Integral Geometry aims to stimulate future research in these areas. Contributors: J. Bernstein,G. Chinta, D. Ciubotaru, J. Faraut, S. Gindikin, J. Jorgenson, J. Kramer, B. Krtz, Y.A. Neretin, K. N ishiyama, O. Offen, H. Schlichtkrull, M.J. Slupinski, R.J. Stanton, B. Speh, P.E. Trapa, T.N.Venkataramana
Note:Springer eBooks
Contents:Preface
On Function Spaces on Symmetric Spaces
A Relation Involving RankinSelberg L
Functions of Cusp Forms and Maass Forms
Orthogonal Period of a Gl3(Z) Eisenstein Series
Regular Orbits of Symmetric Subgroups on Partial Flag Varieties
Helgason's Conjecture in Complex Analytical Interior
Lectures on Lie Algebras
SteinSahi Complementary Series and Their Degenerations
The Special Symplectic Structure of Binary Cubics
On the Restriction of Representations of Sl(2C) to Sl(2,R)
Asymptotics of Spherical Functions for Large Rank: An Introduction
ISBN:9780817648176
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Number theory
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Call number:SPRINGER-2012-9780387847948:ONLINE Show nearby items on shelf
Title:Structure and Geometry of Lie Groups [electronic resource]
Author(s): Joachim Hilgert
Karl-Hermann Neeb
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.Building onthe authors' Lie-Gruppen undLie-Algebren textbook from 1991, itp resents the fundamental principles of Lie groupswhile incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometryin the field. The text is entirely self contained,and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretelyand directly illustratethe correspondence between groups and their Lie algebras. In the second part of the book, theauthorsinvestigate the basic structure and representation theory of finite dimensional Lie algebras,suchasthe rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (ro ot decompositions), and questions related to representation theory. In the third part of the book, the authorsturn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, thefourth part of the book deals with th e structure theory of Lie groups, includingsome refined applications of theexponential function, various classes of Lie groups, andstructural issues for general Lie groups. To round out the book's content, several appendices appear at the end of thislast part. Containing a wealth of useful information,including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups andis a valuable addition to the literature. Prerequisites are generally kept to a minimum , and various pedagogicalfeatures make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more adva
Note:Springer eBooks
Contents:Preface
1 Introduction
Part I Matrix Groups
2 Concrete Matrix Groups
3The Matrix Exponential Function
4Linear Lie Groups
Part II Lie Algebras
5Elementary Structure Theory of Lie Algebras
6Root Decomposition
7Representation Theory of Lie Algebras
Part III Manifolds and Lie Groups
8 Smooth Manifolds
9 Basic Lie Theory
10 Smooth Actions of Lie Groups
Part IV Structure Theory of Lie Groups
11 Normal Subgroups, Nilpotemt and Solvable Lie Groups
12 Compact Lie Groups
13 Semisimple Lie Groups
14 General Structure Theory
15 Complex Lie
ISBN:9780387847948
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Algebraic topology
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Call number:SPRINGER-2011-9783642217449:ONLINE Show nearby items on shelf
Title:Supersymmetry in Mathematics and Physics [electronic resource] : UCLA Los Angeles, USA 2010
Author(s): Sergio Ferrara
Rita Fioresi
V.S Varadarajan
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new developmentin geometry, and mat hematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of thevarious questions raised
Note:Springer eBooks
Contents:Introduction
Black Holes and First Order Flows in Supergravity
Representations of Super Lie Groups: Some Remarks
On Chiral Quantum Superspaces
On the Construction of Chevalley Supergroup
Indecomposable Finite
dimensional Representations of a Class o f Lie algebras and Lie Superalgebras
On the Geometry of Super Riemann Surfaces
Charge Orbits and Moduli Spaces of Black Hole Attractors
Maximal Supersymmetry
Lie Supergroups, Unitary Representations, and Invariant Cones
Geometry of Dual Pairs of Complex Supercurves
On the Superdimension of an Irreducible Representat
ISBN:9783642217449
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2027
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Geometry , Mathematical physics
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Call number:SPRINGER-2011-9783642211478:ONLINE Show nearby items on shelf
Title:p-Adic Lie Groups [electronic resource]
Author(s): Peter Schneider
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with aself-contained and detailed intr oduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets upthe analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition ofLazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings
Note:Springer eBooks
Contents:Introduction
Part A: p
Adic Analysis and Lie Groups
I.Foundations
I.1.Ultrametric Spaces
I.2.Nonarchimedean Fields
I.3.Convergent Series
I.4.Differentiability
I.5.Power Series
I.6.Locally Analytic Functions
II.Manifolds
II.7.Charts and Atlases
II.8.Manifolds
II.9.The Tangent Space
II.10.The Topological Vector Space C^an(M,E), part 1
II.11 Locally Convex K
Vector Spaces
II.12 The Topological Vector Space C^an(M,E), part 2
III.Lie Groups
III.13.Definitions and Foundations
III.14.The Universal Enveloping Algebra
III.15.The Concept of Free
ISBN:9783642211478
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v344
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups
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Call number:SPRINGER-2011-9783642183997:ONLINE Show nearby items on shelf
Title:Homogeneous Spaces and Equivariant Embeddings [electronic resource]
Author(s): D.A Timashev
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standardreasons of algebraic geomet ry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally,open embeddings of a given homogeneous space. S uch equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of combinatorial nature (the Luna-Vusttheory) and description of various geometric and representation-theoretic prop erties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest inthe scope of this book. Spherical varieties include many classical examples, such as Grassmannians , flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the importantissues, including the recent substantial progress obtained in and around the theory of spherical varieties
Note:Springer eBooks
Contents:Introduction
1 Algebraic Homogeneous Spaces
2 Complexity and Rank
3 General Theory of Embeddings
4 Invariant Valuations
5 Spherical Varieties
Appendices
Bibliography
Indices
ISBN:9783642183997
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, 0938-0396 : v138
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups
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Call number:SPRINGER-2011-9783642156274:ONLINE Show nearby items on shelf
Title:Points and Lines [electronic resource] : Characterizing the Classical Geometries
Author(s): Ernest Shult
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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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
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Note:Springer 2013 e-book collections
Note:A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts aresystematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points,as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physicsand gravitation
Note:Springer eBooks
Contents:Introduction
Topology
Manifolds
Tensor Fields
Integration, Homology and Cohomology
Lie Groups
Bundles and Connections
Parallelism, Holonomy, Homotopy and (Co)homology
Riemannian Geometry
Compendium
ISBN:9783642147005
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, Volume 822, 0075-8450 : v822
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematical physics
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Call number:SPRINGER-2011-9783642110122:ONLINE Show nearby items on shelf
Title:Theory of Group Representations and Fourier Analysis [electronic resource]
Author(s): F Gherardelli
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A. Fig Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Reprsentations des groupes linaires p-adiques.- G.W. Mackey: Infinite-dimensional grouprepresentations and their applicati ons
Note:Springer eBooks
Contents:A. Fig Talamanca: Random Fourier series on compact groups
S. Helgason: Representations of semisimple Lie groups
H. Jacquet: Reprsentations des groupes linaires p
adiques
G.W. Mackey: Infinite
dimensional group representations and their applications
ISBN:9783642110122
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v53
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
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Call number:SPRINGER-2011-9783642109379:ONLINE Show nearby items on shelf
Title:Gruppi, anelli di Lie e teoria della coomologia [electronic resource]
Author(s): G Zappa
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:R. Baer: Complementation in finite gropus.- M. Lazard: Groupes, anneaux de Lie et problme de Burnside.- J. Tits: Sur les groupes algbriques afffines. Thormes fondamentaux de structure. Classification des groupessemisimples et gomtries associes
Note:Springer eBooks
Contents:R. Baer: Complementation in finite gropus
M. Lazard: Groupes, anneaux de Lie et problme de Burnside
J. Tits: Sur les groupes algbriques afffines. Thormes fondamentaux de structure. Classification des groupes semisimples et gomtries associes
ISBN:9783642109379
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v20
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Topological Groups
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Call number:SPRINGER-2011-9781441974006:ONLINE Show nearby items on shelf
Title:An Introduction to Manifolds [electronic resource]
Author(s): Loring W Tu
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classicalmechanics, general relativity , and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By theend of the book the reader should be able to comput e, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessaryfor further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for aone-semester graduate or advanced undergraduate course, as well as by students engaged in sel f-study. The requisite point-set topology is included in an appendix of twenty-five pages other appendices review facts from real analysisand linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal un dergraduate prerequisites, An Introduction to Manifolds is also an excellent foundation for the author'spublication with Raoul Bott, Differential Forms in Algebraic Topology.
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
Chapter 1. Euclidean Spaces
Chapter 2. Manifolds
Chapter 3. The Tangent Space
Chapter 4. Lie Groups and Lie Algebras
Chapter 5. Differential Forms
Chapter 6. Integration
Chapter 7. De Rham Theory
Appendices
A. Point
Set Topology
B. The Inverse Function Theorem on R(N) and Related Results
C. Existence of a Partition of Unity in General
D. Linear Algebra
E. Quaternions and the Symplectic Group
Solutions to Selected Exercises
Hints and Solutions to Selected End
of
Section Problems
List of Sym
ISBN:9781441974006
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9781441972545:ONLINE Show nearby items on shelf
Title:Topology, Geometry and Gauge fields [electronic resource] : Foundations
Author(s): Gregory L Naber
Date:2011
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The authors point of view is that the rekindled interest that mathematics andphysics have shown in ea ch other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and thetopological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementarypronouncements of quantum mechanics, and a solid background in real analy sis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topologicalspace and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 w ith instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outliningDonaldsons beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: It is unusual to find a book so carefully tailoredto the needs of this interdisciplinary area of mathematical physicsNaber combines a deep knowledge of his subject with an excellent informal writi ng style. (NZMS Newsletter) ...this book should be very interesting formathematicians and physicists (as well as other scientists) who are concerned with gauge theories. (ZENTRALBLATT FUER MATHEMATIK) The book is well written and the examples do a great s ervice to the reader. It will be a helpfulcompanion to anyone teaching or studying gauge theory (Mathematical Reviews)
Note:Springer eBooks
Contents:Contents: Preface
Physical and geometrical motivation 1 Topological spaces
Homotopy groups
Principal bundles
Differentiable manifolds and matrix Lie groups
Gauge fields and Instantons. Appendix. References. Index
ISBN:9781441972545
Series:e-books
Series:SpringerLink (Online service)
Series:Texts in Applied Mathematics, 0939-2475 : v25
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Topology , Quantum theory
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Call number:SPRINGER-2011-9781441960559:ONLINE Show nearby items on shelf
Title:Integral Geometry and Radon Transforms [electronic resource]
Author(s): Sigurdur Helgason
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In this text, integral geometry deals with Radons problem of representing a function on a manifold in terms of its integrals over certain submanifoldshence the term the Radon transform. Examples and far-reachinggeneralizations lead to fundamental pro blems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case ofthe plane, the inversion theorem and the support theorem ha ve had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroomuse or self-study. A number of exercises point to further results with document ation. From the reviews: Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book isconcentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area. Boris Rubin,Louisiana State University
Note:Springer eBooks
Contents:The Radon Transformon Rn
A Duality in Integral Geometry
The Radon Transform on Two
Point Homogeneous Spaces
The X
Ray Transform on a Symmetric Space
Orbital Integrals
The Mean
Value Operator
Fourier Transforms and Distribution: A Rapid Course
Lie Transformation Groups and Differential Operators
Bibliography
Notational Conventions
Index
ISBN:9781441960559
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Integral Transforms , Global differential geometry
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Call number:SPRINGER-2011-9780857291608:ONLINE Show nearby items on shelf
Title:Representation Theory of the Virasoro Algebra [electronic resource]
Author(s): Kenji Iohara
Yoshiyuki Koga
Date:2011
Publisher:London : Springer London
Size:1 online resource
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Note:The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of theVirasoro algebra in a self- contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebrasassociated to the so-called minimal series represe ntations. Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. Fundamental resultsareorganizedin a unified way and existing proofs refined. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widelybelieved to be true, are collated, and results which are known but not verified are proven, such as the corrected s tructure theorem of Fock modules in chapter eight. This book will be of interest to a wide range of mathematicians andphysicists from the level of graduate students to researchers
Note:Springer eBooks
Contents:Preliminary
Classification of Harish
Chandra Modules
The Jantzen Filtration
Determinant Formulae
Verma Modules I: Preliminaries
Verma Modules II: Structure Theorem
A Duality among Verma Modules
Fock Modules
Rational Vertex Operator Algebras
Coset Constructions for sl2
Unitarisable Harish
Chandra Modules
Homological Algebras
Lie p
algebras
Vertex Operator Algebras
ISBN:9780857291608
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Functions, special , Combinatorics
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Call number:SPRINGER-2011-9780857290212:ONLINE Show nearby items on shelf
Title:Ergodic Theory [electronic resource] : with a view towards Number Theory
Author(s): Manfred Einsiedler
Thomas Ward
Date:2011
Publisher:London : Springer London
Size:1 online resource
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Note:This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describesome recent application s to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between thecontinued fraction map and the modular surface , and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory andfunctional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory,homogenous dynamics or number theory
Note:Springer eBooks
Contents:Motivation
Ergodicity, Recurrence and Mixing
Continued Fractions
Invariant Measures for Continuous Maps
Conditional Measures and Algebras
Factors and Joinings
Furstenbergs Proof of Szemeredis Theorem
Actions of Locally Compact Groups
Geodesic Flow on Quotients of the Hyperbolic Plane
Nilrotation
More Dynamics on Quotients of the Hyperbolic Plane
Appendix A: Measure Theory
Appendix B: Functional Analysis
Appendix C: Topological Groups
ISBN:9780857290212
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v259
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Number theory
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Call number:SPRINGER-2011-9780817647414:ONLINE Show nearby items on shelf
Title:Developments and Trends in Infinite-Dimensional Lie Theory [electronic resource]
Author(s): Karl-Hermann Neeb
Arturo Pianzola
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts:infinite-dimensional Lie ( super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representationtheory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and KacMoody superalgebras.The articles in Part (B) examine connections between infinite-dimension al Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, toJordan-theoretic geometries and new results on direct-limit groups. The analytic representation theor y of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods basedon heat kernels, multiplicity freeness, BanachLiePoisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Belti, W. Bertram, J. Faulkner, Ph. Gille, H. Glckner, K.-H.Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf
Note:Springer eBooks
Contents:Preface
Part A: Infinite
Dimensional Lie (Super
)Algebras
Isotopy for Extended Affine Lie Algebras and Lie Tori
Remarks on the Isotriviality of Multiloop Algebras
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras A Survey
Tensor Representations of Classical Locally Finite Lie Algebras
Lie Algebras, Vertex Algebras, and Automorphic Forms
KacMoody Superalgebras and Integrability
Part B: Geometry of Infinite
Dimensional Lie (Transformation) Groups
Jordan Structures and Non
Associative Geometry
Direct Limits of Infinite
Dimensional L
ISBN:9780817647414
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v288
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory , Topological Groups , Geometry
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Call number:SPRINGER-2011-9780817647353:ONLINE Show nearby items on shelf
Title:Higher Structures in Geometry and Physics [electronic resource] : In Honor of Murray Gerstenhaber and Jim Stasheff
Author(s): Alberto S Cattaneo
Anthony Giaquinto
Ping Xu
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics such as algebra, algebraic topology, differentialgeometry, algebraic geome try, mathematical physics and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformationquantization, theory of algebroids and groupoids, symplec tic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role inrecent mathematical advances. For example, algebraic versions of higher homotopi es have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations anddeformation philosophy, a basic observation is that higher homotopy structures behave much better than st rict structures. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometryand Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures. Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto,S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble
Note:Springer eBooks
Contents:Topics in Algebraic deformation theory
Origins and breadth of the theory of higher homotopies
The deformation philosophy, quantization and noncommutative space
time structures
Differential geometry of Gerbes and differential forms
Symplectic connections of Ricci type and star products
Effective BatalinVilkovisky theories, equivariant configuration spaces and cyclic chains
Noncommutative calculus and the Gauss
Manin connection
The Lie algebra perturbation lemma
Twisting Elements in Homotopy G
algebras
Homological perturbation theory and homological mirror symmetry
ISBN:9780817647353
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v287
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Topological Groups , Mathematical physics
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Call number:SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics
Author(s): Michael Ruzhansky
Ville Turunen
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises
Note:Springer eBooks
Contents:Preface
Introduction
Part I Foundations of Analysis
A Sets, Topology and Metrics
B Elementary Functional Analysis
C Measure Theory and Integration
D Algebras
Part II Commutative Symmetries
1 Fourier Analysis on Rn
2 Pseudo
differential Operators on Rn
3 Periodic and Discrete Analysis
4 Pseudo
differential Operators on Tn
5 Commutator Characterisation of Pseudo
differential Operators
Part III Representation Theory of Compact Groups
6 Groups
7 Topological Groups
8 Linear Lie Groups
9 Hopf Algebras
Part IV Non
commutative Symmetries
10 Pseu
ISBN:9783764385149
Series:e-books
Series:SpringerLink (Online service)
Series:Pseudo-Differential Operators, Theory and Applications : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Differential equations, partial
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Call number:SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf
Title:Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures
Author(s): Leonid Positselski
Date:2010
Publisher:Basel : Springer Basel
Size:1 online resource
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Note:This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists
Note:Springer eBooks
Contents:Preface
Introduction
0 Preliminaries and Summary
1 Semialgebras and Semitensor Product
2 Derived Functor SemiTor
3 Semicontramodules and Semihomomorphisms
4 Derived Functor SemiExt
5 Comodule
Contramodule Correspondence
6 Semimodule
Semicontramodule Correspondence
7 Functoriality in the Coring
8 Functoriality in the Semialgebra
9 Closed Model Category Structures
10 A Construction of Semialgebras
11 Relative Nonhomogeneous Koszul Duality
Appendix A Contramodules over Coalgebras over Fields
Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se
ISBN:9783034604369
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Series:Monografie Matematyczne : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry
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Call number:SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf
Title:Representation Theory and Complex Geometry [electronic resource]
Author(s): Neil Chriss
Victor Ginzburg
Date:2010
Edition:1st
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews
Note:Springer eBooks
Contents:Preface
Chapter 0. Introduction
Chapter 1. Symplectic Geometry
Chapter 2. Mosaic
Chapter 3. Complex Semisimple Groups
Chapter 4. Springer Theory
Chapter 5. Equivariant K
Theory
Chapter 6. Flag Varieties, K
Theory, and Harmonic Polynomials
Chapter 7. Hecke Algebras and K
Theory
Chapter 8. Representations of Convolution Algebras
Bibliography
ISBN:9780817649388
Series:e-books
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Series:Modern Birkhuser Classics
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Keywords: Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics
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Call number:SPRINGER-2010-9780817649340:ONLINE Show nearby items on shelf
Title:Cohomological and Geometric Approaches to Rationality Problems [electronic resource] : New Perspectives
Author(s): Fedor Bogomolov
Yuri Tschinkel
Date:2010
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, or geometrically, on the dimension of the variety. A major success in 19th century algebraicgeometry was a complete sol ution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. These advances have led to many interdisciplinary applications of algebraic geometry.This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality ofmoduli spaces of curves, and rational points on algebraic varieties. Th is volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems. I. Bauer C.Bhning F. Bogomolov F. Catanese I. Cheltsov N. Hoffmann S.-J. Hu M.-C. Kang L. Katzarkov B. Kuny avskii A. Kuznetsov J. Park T. Petrov Yu. G. Prokhorov A.V. Pukhlikov Yu. Tschinkel
Note:Springer eBooks
Contents:The Rationality of Certain Moduli Spaces of Curves of Genus 3
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo
Unramified Cohomology of Finite Groups of Lie Type
Sextic Double Solids
Moduli Stacks of Vector Bundles on Curves and the KingSchofield Rationality Proof
Noethers Problem for Some
Groups
Generalized Homological Mirror Symmetry and Rationality Questions
The Bogomolov Multiplier of Finite Simple Groups
Derived Categories of Cubic Fourfolds
Fields of Invariants of Finite Linear Groups
The Rationality Problem and Birational Rig
ISBN:9780817649340
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v282
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Topological Groups
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Call number:SPRINGER-2010-9780817647179:ONLINE Show nearby items on shelf
Title:Introduction to Quantum Groups [electronic resource]
Author(s): George Lusztig
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specializedat roots of 1 and yiel d new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of thetheory are provided with canonical bases h aving rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includesthe case of quantum affine enveloping algebras and, more generall y, the quantum analogs of the KacMoody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Liegroups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Si nce large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook.**************************************** There is no doubt that this volume is a very remarkable piece of work...Its appearance represen ts a landmark in the mathematical literature. Bulletin of the London Mathematical Society Thisbook is an important contribution to the field and can be recommended especially to mathematicians working in the field. EMS Newsletter The present book gives a very efficient presentation of an important part of quantum grouptheory. It is a valuable contribution to the literature. Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard re ference book for the material presentedand anyone interested in the DrinfeldJimbo algebras will have to study it very carefully. ZAA [T]his book is much more than an 'introduction to q
Note:Springer eBooks
Contents:Preface
Part I: The Drinfeld
Jimbo Algebra U
Part II: Geometric Realization of f
Part III: Kashiwaras Operators and Applications
Part IV: Canonical Basis of U
Part V: Change of Rings
Part VI: Braid Group Action
Index of Notation
Index of Terminology
ISBN:9780817647179
Series:e-books
Series:SpringerLink (Online service)
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Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Topological Groups , Quantum theory , Mathematical physics
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Call number:SPRINGER-2010-9780817646974:ONLINE Show nearby items on shelf
Title:Representation Theory of Algebraic Groups and Quantum Groups [electronic resource]
Author(s): Akihiko Gyoja
Hiraku Nakajima
Ken-ichi Shinoda
Toshiaki Shoji
Toshiyuki Tanisaki
Date:2010
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras,representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection groups and associated Hecke algebras. Representation Theory of Algebraic Groups andQuantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors: H. H. Andersen, S. Ariki, C. Bonnaf, J. Chuang, J. Du, M.Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. La m, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang
Note:Springer eBooks
ISBN:9780817646974
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v284
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Algebra , Topological Groups , Number theory , Mathematical physics
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Call number:SPRINGER-2009-9789491216367:ONLINE Show nearby items on shelf
Title:Topics in Measure Theory and Real Analysis [electronic resource]
Author(s): Alexander B Kharazishvili
Date:2009
Publisher:Paris : Atlantis Press
Size:1 online resource
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Note:This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measureextension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methodsare presented for solving the above mentio ned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures onsolvable uncountable groups non-separable extensions of invariant mea sures are constructed by using their ergodic components absolutely non-measurable additive functionals are constructed for certain classes of measures thestructure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). Newresults and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory an d general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin andSierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric sp aces, and so on. Essential information on these topics is also included in the text(primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only al lows the book to be used as a monograph but also as a course oflectures for students whose interests lie in set theory, real analysis, measure theory and general topology
Note:Springer eBooks
ISBN:9789491216367
Series:e-books
Series:SpringerLink (Online service)
Series:Atlantis Studies in Mathematics, 1875-7634 : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2009-9783540853329:ONLINE Show nearby items on shelf
Title:Generalized Lie Theory in Mathematics, Physics and Beyond [electronic resource]
Author(s): Sergei Silvestrov
Eugen Paal
Viktor Abramov
Alexander Stolin
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to theinterplay between severa l rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensionsof differential calculus and geometry, non-ass ociative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book will be a useful source ofinspiration for a broad spectrum of researchers and for research students , and includes contributions from several large research communities in modern mathematics and physics. This volume consists of 5 parts comprising 25 chapters,which were contributed by 32 researchers from 12 different countries. All contributions in the v olume have been refereed
Note:Springer eBooks
Contents:Non
Associative and Non
Commutative Structures for Physics
Moufang Transformations and Noether Currents
Weakly Nonassociative Algebras, Riccati and KP Hierarchies
Applications of Transvectants
Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics
A Rewriting Approach to Graph Invariants
Non
Commutative Deformations, Quantization, Homological Methods, and Representations
Graded q
Differential Algebra Approach to q
Connection
On Generalized N
Complexes Coming from Twisted Derivations
Remarks on Quantizations, Words and R
Matrices
Conn
ISBN:9783540853329
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Mathematical physics
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Call number:SPRINGER-2009-9783540772637:ONLINE Show nearby items on shelf
Title:The Geometry of Infinite-Dimensional Groups [electronic resource]
Author(s): Boris Khesin
Robert Wendt
Date:2009
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. Whileinfinite-dimensional groups often exh ibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjointorbits to knot theory, from optimal mass transport to moduli sp aces of flat connections on surfaces. The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry,and Hamiltonian systems
Note:Springer eBooks
Contents:Preface
Introduction
I Preliminaries
II Infinite
dimensional Lie Groups: Their Geometry, Orbits and Dynamical Systems
III Applications of Groups: Topological and Holomorphic Gauge Theories
Appendices
A1 Root Systems
A2 Compact Lie Groups
A3 Krichever
Novikov Algebras
A4 Khler Structures on the Virasoro and Loop Group Coadjoint Orbits
A5 Metrics and Diameters of the Group of Hamiltonian Diffeomorphisms
A6 Semi
Direct Extensions of the Diffeomorphism Group and Gas Dynamics
A7 The Drinfeld
Sokolov Reduction
A8 Surjectivity of the Exponential Map on Pseudo
ISBN:9783540772637
Series:e-books
Series:SpringerLink (Online service)
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics : v51
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Global analysis , Mathematical physics , Thermodynamics
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