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Author : Meinolf Geck,Gunter Malle
Publisher : Cambridge University Press
Page : 405 pages
File Size : 53,9 Mb
Release : 2020-02-27
Category : Mathematics
ISBN : 9781108489621
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.
Author : François Digne,Jean Michel
Publisher : Cambridge University Press
Page : 267 pages
File Size : 53,5 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9781108481489
An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Author : Gunter Malle,Donna Testerman
Publisher : Cambridge University Press
Page : 324 pages
File Size : 44,7 Mb
Release : 2011-09-08
Category : Mathematics
ISBN : 9781139499538
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Author : David A. Craven
Publisher : Springer Nature
Page : 294 pages
File Size : 44,8 Mb
Release : 2019-08-30
Category : Mathematics
ISBN : 9783030217921
This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.
Author : Roger W. Carter
Publisher : Unknown
Page : 570 pages
File Size : 53,7 Mb
Release : 1993-08-24
Category : Mathematics
ISBN : UOM:39015051265109
The finite groups of Lie type are of basic importance in the theory of groups. A classic in its field, this book presents the theories of finite groups of Lie type in a clear and accessible style, especially with regard to the main concepts of the theory and the techniques of proof used, and gives a detailed exposition of the complex representation theory.
Author : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 51,7 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781107162396
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 : Roger William Carter
Publisher : Cambridge University Press
Page : 662 pages
File Size : 40,8 Mb
Release : 2005-10-27
Category : Mathematics
ISBN : 0521851386
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 260 pages
File Size : 45,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0521674549
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Author : Roger William Carter
Publisher : Unknown
Page : 70 pages
File Size : 52,7 Mb
Release : 1977
Category : Finite groups
ISBN : UOM:39015015458568
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 49,5 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
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 : 44,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511
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 : B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103299
This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
Author : Daniel Gorenstein
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 43,9 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781468484977
In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in 1962, which stated that every finite group of odd order (D2) is solvable (D3)-a statement expressi ble in a single line, yet its proof required a full 255-page issue of the Pacific 10urnal of Mathematics [93]. Soon thereafter, in 1965, came the first new sporadic simple group in over 100 years, the Zvonimir Janko group 1 , to further stimulate the 1 'To make the book as self-contained as possible. we are including definitions of various terms as they occur in the text. However. in order not to disrupt the continuity of the discussion. we have placed them at the end of the Introduction. We denote these definitions by (DI). (D2), (D3). etc.
Author : Roger W. Carter,Meinolf Geck
Publisher : Cambridge University Press
Page : 203 pages
File Size : 42,6 Mb
Release : 1998-09-03
Category : Mathematics
ISBN : 9780521643252
This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Author : Meinolf Geck,Götz Pfeiffer
Publisher : Oxford University Press
Page : 478 pages
File Size : 51,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0198502508
Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.
