Linear Representations Of Groups
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Author |
: E.B. Vinberg |
Publisher |
: Birkhäuser |
Total Pages |
: 151 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034892742 |
ISBN-13 |
: 3034892748 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Linear Representations of Groups by : E.B. Vinberg
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Author |
: Jean Pierre Serre |
Publisher |
: |
Total Pages |
: 170 |
Release |
: 1996 |
ISBN-10 |
: OCLC:806314847 |
ISBN-13 |
: |
Rating |
: 4/5 (47 Downloads) |
Synopsis Linear Representations of Finite Groups by : Jean Pierre Serre
Author |
: Jean-Pierre Serre |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 178 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468494587 |
ISBN-13 |
: 1468494589 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Linear Representations of Finite Groups by : Jean-Pierre Serre
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.
Author |
: Pavel I. Etingof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 2011 |
ISBN-10 |
: 9780821853511 |
ISBN-13 |
: 0821853511 |
Rating |
: 4/5 (11 Downloads) |
Synopsis Introduction to Representation Theory by : Pavel I. Etingof
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 |
: Ėrnest Borisovich Vinberg |
Publisher |
: Birkhauser |
Total Pages |
: 146 |
Release |
: 1989 |
ISBN-10 |
: 0817622888 |
ISBN-13 |
: 9780817622886 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Linear Representations of Groups by : Ėrnest Borisovich Vinberg
Author |
: M. A. Naimark |
Publisher |
: Elsevier |
Total Pages |
: 465 |
Release |
: 2014-07-15 |
ISBN-10 |
: 9781483184982 |
ISBN-13 |
: 1483184986 |
Rating |
: 4/5 (82 Downloads) |
Synopsis Linear Representations of the Lorentz Group by : M. A. Naimark
Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.
Author |
: Peter Webb |
Publisher |
: Cambridge University Press |
Total Pages |
: 339 |
Release |
: 2016-08-19 |
ISBN-10 |
: 9781107162396 |
ISBN-13 |
: 1107162394 |
Rating |
: 4/5 (96 Downloads) |
Synopsis A Course in Finite Group Representation Theory by : Peter Webb
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 |
: Ernest B. Vinberg |
Publisher |
: Birkhäuser |
Total Pages |
: 146 |
Release |
: 2013-01-02 |
ISBN-10 |
: 3034800649 |
ISBN-13 |
: 9783034800648 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Linear Representations of Groups by : Ernest B. Vinberg
This book gives an exposition of the fundamentals of the theory of linear representations of ?nite and compact groups, as well as elements of the t- ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the ?eld under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of ?nite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely - pliedbranchesof algebra. Practically every timethatgroupsareencountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. 0. Basic Notions 0. 1.
Author |
: Gordon James |
Publisher |
: Cambridge University Press |
Total Pages |
: 436 |
Release |
: 2001-10-18 |
ISBN-10 |
: 9781139811057 |
ISBN-13 |
: 1139811053 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Representations and Characters of Groups by : Gordon James
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 |
: Alexander Kleshchev |
Publisher |
: Cambridge University Press |
Total Pages |
: 293 |
Release |
: 2005-06-30 |
ISBN-10 |
: 9781139444064 |
ISBN-13 |
: 1139444069 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Linear and Projective Representations of Symmetric Groups by : Alexander Kleshchev
The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own