Principal Structures and Methods of Representation Theory

Principal Structures and Methods of Representation Theory
Author: Dmitriĭ Petrovich Zhelobenko
Publsiher: American Mathematical Soc.
Total Pages: 430
Release: 2022
ISBN: 9780821889671
Category: Mathematics
Language: EN, FR, DE, ES & NL

Principal Structures and Methods of Representation Theory Book Excerpt:

The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups,along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Liealgebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.

Representation Theory of Finite Monoids

Representation Theory of Finite Monoids
Author: Benjamin Steinberg
Publsiher: Springer
Total Pages: 320
Release: 2016-12-09
ISBN: 3319439324
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory of Finite Monoids Book Excerpt:

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.

Representation Theory

Representation Theory
Author: Edwin Williams
Publsiher: MIT Press
Total Pages: 295
Release: 2002-12-20
ISBN: 9780262265072
Category: Language Arts & Disciplines
Language: EN, FR, DE, ES & NL

Representation Theory Book Excerpt:

In this theoretical monograph, Edwin Williams demonstrates that when syntax is economical, it economizes on shape distortion rather than on distance. According to Williams, this new notion of economy calls for a new architecture for the grammatical system—in fact, for a new notion of derivation. The new architecture offers a style of clausal embedding—the Level Embedding Scheme—that predictively ties together the locality, reconstructive behavior, and "target" type of any syntactic process in a way that is unique to the model. Williams calls his theory "Representation Theory" to put the notion of economy at the forefront. Syntax, in this theory, is a series of representations of one sublanguage in another.

Vector Bundles and Representation Theory

Vector Bundles and Representation Theory
Author: Vector Bundles Conference on Hilbert Schemes
Publsiher: American Mathematical Soc.
Total Pages: 244
Release: 2003
ISBN: 0821832646
Category: Mathematics
Language: EN, FR, DE, ES & NL

Vector Bundles and Representation Theory Book Excerpt:

This volume contains 13 papers from the conference on 'Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory'. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S^1$ fixed points in Quot-schemes and mirror principle computations for Grassmannians by S.T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Algebra Representation Theory

Algebra   Representation Theory
Author: Klaus W. Roggenkamp,Mirela Stefanescu
Publsiher: Springer Science & Business Media
Total Pages: 460
Release: 2001-08-31
ISBN: 9780792371137
Category: Mathematics
Language: EN, FR, DE, ES & NL

Algebra Representation Theory Book Excerpt:

Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.

Representation Theory and Beyond

Representation Theory and Beyond
Author: Jan Šťovíček,Jan Trlifaj
Publsiher: American Mathematical Soc.
Total Pages: 298
Release: 2020-11-13
ISBN: 147045131X
Category: Education
Language: EN, FR, DE, ES & NL

Representation Theory and Beyond Book Excerpt:

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Basic Representation Theory of Algebras

Basic Representation Theory of Algebras
Author: Ibrahim Assem,Flávio U. Coelho
Publsiher: Springer Nature
Total Pages: 311
Release: 2020-04-03
ISBN: 3030351181
Category: Mathematics
Language: EN, FR, DE, ES & NL

Basic Representation Theory of Algebras Book Excerpt:

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

A Tour of Representation Theory

A Tour of Representation Theory
Author: Martin Lorenz
Publsiher: American Mathematical Soc.
Total Pages: 654
Release: 2018
ISBN: 1470436809
Category: Categories (Mathematics)
Language: EN, FR, DE, ES & NL

A Tour of Representation Theory Book Excerpt:

Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.

Symmetry Representation Theory and Its Applications

Symmetry  Representation Theory and Its Applications
Author: Roger Howe,Markus Hunziker,Jeb F. Willenbring
Publsiher: Springer
Total Pages: 538
Release: 2015-01-04
ISBN: 1493915908
Category: Mathematics
Language: EN, FR, DE, ES & NL

Symmetry Representation Theory and Its Applications Book Excerpt:

Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

Operators and Representation Theory

Operators and Representation Theory
Author: Palle E.T. Jorgensen
Publsiher: Courier Dover Publications
Total Pages: 304
Release: 2017-05-22
ISBN: 0486822575
Category: Science
Language: EN, FR, DE, ES & NL

Operators and Representation Theory Book Excerpt:

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Surveys in Representation Theory of Algebras

Surveys in Representation Theory of Algebras
Author: Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Publsiher: American Mathematical Soc.
Total Pages: 203
Release: 2018-09-12
ISBN: 1470436795
Category: Representations of algebras
Language: EN, FR, DE, ES & NL

Surveys in Representation Theory of Algebras Book Excerpt:

This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

The Representation Theory of Finite Groups

The Representation Theory of Finite Groups
Author: W. Feit
Publsiher: Elsevier
Total Pages: 501
Release: 1982-05-01
ISBN: 9780080960135
Category: Computers
Language: EN, FR, DE, ES & NL

The Representation Theory of Finite Groups Book Excerpt:

The Representation Theory of Finite Groups

Integral Geometry and Representation Theory

Integral Geometry and Representation Theory
Author: I. M. Gel'fand,M. I. Graev,N. Ya. Vilenkin
Publsiher: Academic Press
Total Pages: 468
Release: 2014-05-12
ISBN: 1483262251
Category: Mathematics
Language: EN, FR, DE, ES & NL

Integral Geometry and Representation Theory Book Excerpt:

Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups
Author: Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publsiher: Cambridge University Press
Total Pages: 180
Release: 2014-01-16
ISBN: 1107729912
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups Book Excerpt:

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

Representation Theory of Finite Groups

Representation Theory of Finite Groups
Author: Martin Burrow
Publsiher: Courier Corporation
Total Pages: 185
Release: 1965
ISBN: 0486674878
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory of Finite Groups Book Excerpt:

Concise, graduate-level exposition of the theory of finite groups, including the theory of modular representations. Topics include representation theory of rings with identity, representation theory of finite groups, applications of the theory of characters, construction of irreducible representations and modular representations. Rudiments of linear algebra and knowledge of group theory helpful prerequisites. Exercises. Bibliography. Appendix. 1965 edition.

Representation Theories and Algebraic Geometry

Representation Theories and Algebraic Geometry
Author: A. Broer
Publsiher: Springer Science & Business Media
Total Pages: 444
Release: 2013-03-09
ISBN: 9401591318
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theories and Algebraic Geometry Book Excerpt:

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Geometry of Moduli Spaces and Representation Theory

Geometry of Moduli Spaces and Representation Theory
Author: Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publsiher: American Mathematical Soc.
Total Pages: 436
Release: 2017-12-15
ISBN: 1470435748
Category: Algebraic varieties
Language: EN, FR, DE, ES & NL

Geometry of Moduli Spaces and Representation Theory Book Excerpt:

This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.

Elements of the Representation Theory of the Jacobi Group

Elements of the Representation Theory of the Jacobi Group
Author: Rolf Berndt,Ralf Schmidt
Publsiher: Springer Science & Business Media
Total Pages: 213
Release: 2012-01-03
ISBN: 3034802838
Category: Mathematics
Language: EN, FR, DE, ES & NL

Elements of the Representation Theory of the Jacobi Group Book Excerpt:

Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.

Representation Theory of Finite Groups and Related Topics

Representation Theory of Finite Groups and Related Topics
Author: Irving Reiner,American Mathematical Society
Publsiher: American Mathematical Soc.
Total Pages: 178
Release: 1971
ISBN: 0821814214
Category: Mathematics
Language: EN, FR, DE, ES & NL

Representation Theory of Finite Groups and Related Topics Book Excerpt:

Curvature Scale Space Representation Theory Applications and MPEG 7 Standardization

Curvature Scale Space Representation  Theory  Applications  and MPEG 7 Standardization
Author: F. Mokhtarian,M. Bober
Publsiher: Springer Science & Business Media
Total Pages: 431
Release: 2013-11-11
ISBN: 9401703434
Category: Computers
Language: EN, FR, DE, ES & NL

Curvature Scale Space Representation Theory Applications and MPEG 7 Standardization Book Excerpt:

MPEG-7 is the first international standard which contains a number of key techniques from Computer Vision and Image Processing. The Curvature Scale Space technique was selected as a contour shape descriptor for MPEG-7 after substantial and comprehensive testing, which demonstrated the superior performance of the CSS-based descriptor. Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization is based on key publications on the CSS technique, as well as its multiple applications and generalizations. The goal was to ensure that the reader will have access to the most fundamental results concerning the CSS method in one volume. These results have been categorized into a number of chapters to reflect their focus as well as content. The book also includes a chapter on the development of the CSS technique within MPEG standardization, including details of the MPEG-7 testing and evaluation processes which led to the selection of the CSS shape descriptor for the standard. The book can be used as a supplementary textbook by any university or institution offering courses in computer and information science.