Theory Of Group Representations

Author : M.A. Naimark,A.I Stern
Publisher : Springer
Page : 0 pages
File Size : 42,8 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 1461381444

Get Book

Theory of Group Representations by M.A. Naimark,A.I Stern Pdf

Author's Preface to the Russian Edition This book is written for advanced students, for predoctoral graduate stu dents, and for professional scientists-mathematicians, physicists, and chemists-who desire to study the foundations of the theory of finite dimensional representations of groups. We suppose that the reader is familiar with linear algebra, with elementary mathematical analysis, and with the theory of analytic functions. All else that is needed for reading this book is set down in the book where it is needed or is provided for by references to standard texts. The first two chapters are devoted to the algebraic aspects of the theory of representations and to representations of finite groups. Later chapters take up the principal facts about representations of topological groups, as well as the theory of Lie groups and Lie algebras and their representations. We have arranged our material to help the reader to master first the easier parts of the theory and later the more difficult. In the author's opinion, however, it is algebra that lies at the heart of the whole theory. To keep the size of the book within reasonable bounds, we have limited ourselves to finite-dimensional representations. The author intends to devote another volume to a more general theory, which includes infinite dimensional representations.

Author : J.L. Alperin,Rowen B. Bell
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207993

Get Book

Groups and Representations by J.L. Alperin,Rowen B. Bell Pdf

A concise treatment of topics from group theory and representation theory for use in a one-term course. Focussing on the non-commutative side of the field, this advanced textbook emphasizes the general linear group as the most important group and example. Readers are expected to be familiar with groups, rings, and fields, and to have a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to introduce the reader to additional topics.

Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 42,7 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178

Get Book

Theory of Group Representations and Applications by Asim Orhan Barut,Ryszard R?czka Pdf

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 53,8 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

Get Book

Quantum Theory, Groups and Representations by Peter Woit Pdf

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Author : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 44,7 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396

Get Book

A Course in Finite Group Representation Theory by Peter Webb Pdf

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Author : Emmanuel Kowalski
Publisher : American Mathematical Society
Page : 442 pages
File Size : 50,8 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409661

Get Book

An Introduction to the Representation Theory of Groups by Emmanuel Kowalski Pdf

Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 43,7 Mb
Release : 2011-10-23
Category : Mathematics
ISBN : 9781461407768

Get Book

Representation Theory of Finite Groups by Benjamin Steinberg Pdf

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Author : Yurii I. Lyubich
Publisher : Birkhäuser
Page : 231 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891691

Get Book

Introduction to the Theory of Banach Representations of Groups by Yurii I. Lyubich Pdf

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.

Author : Dudley Ernest Littlewood
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 45,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821840672

Get Book

The Theory of Group Characters and Matrix Representations of Groups by Dudley Ernest Littlewood Pdf

Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.

Author : Alexander Zimmermann
Publisher : Springer
Page : 720 pages
File Size : 49,6 Mb
Release : 2014-08-15
Category : Mathematics
ISBN : 9783319079684

Get Book

Representation Theory by Alexander Zimmermann Pdf

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

Author : Gordon James,Martin Liebeck
Publisher : Cambridge University Press
Page : 436 pages
File Size : 43,8 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 9781139811057

Get Book

Representations and Characters of Groups by Gordon James,Martin Liebeck Pdf

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

Author : A. A. Kirillov
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642662430

Get Book

Elements of the Theory of Representations by A. A. Kirillov Pdf

The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.

Author : A Barut,R Raczka
Publisher : World Scientific Publishing Company
Page : 740 pages
File Size : 40,7 Mb
Release : 1986-11-01
Category : Mathematics
ISBN : 9789813103870

Get Book

Theory of Group Representations and Applications by A Barut,R Raczka Pdf

The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 44,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

Get Book

Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Author : Persi Diaconis
Publisher : Ims
Page : 212 pages
File Size : 44,9 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015014354511

Get Book

Group Representations in Probability and Statistics by Persi Diaconis Pdf