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Author : François Digne,Jean Michel
Publisher : Cambridge University Press
Page : 267 pages
File Size : 44,9 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 : François Digne,Jean Michel
Publisher : Cambridge University Press
Page : 172 pages
File Size : 40,9 Mb
Release : 1991-04-26
Category : Mathematics
ISBN : 052140648X
The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.
Author : Meinolf Geck,Gunter Malle
Publisher : Cambridge University Press
Page : 405 pages
File Size : 42,7 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 : James E. Humphreys
Publisher : Cambridge University Press
Page : 260 pages
File Size : 41,7 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 : David A. Craven
Publisher : Springer Nature
Page : 294 pages
File Size : 46,7 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 : Gunter Malle,Donna Testerman
Publisher : Cambridge University Press
Page : 324 pages
File Size : 48,8 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 : Peter Webb
Publisher : Cambridge University Press
Page : 339 pages
File Size : 55,9 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 W. Carter
Publisher : Unknown
Page : 570 pages
File Size : 50,6 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 : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 50,6 Mb
Release : 2003
Category : Linear algebraic groups
ISBN : 9780821843772
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author : Roger W. Carter,Meinolf Geck
Publisher : Cambridge University Press
Page : 203 pages
File Size : 50,8 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 : Roger William Carter
Publisher : Cambridge University Press
Page : 662 pages
File Size : 55,5 Mb
Release : 2005-10-27
Category : Mathematics
ISBN : 0521851386
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 41,8 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Author : François Digne,Jean Michel
Publisher : Unknown
Page : 168 pages
File Size : 45,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107088240
In this book, which is based on a graduate course taught at the University of Paris, the authors aim to treat the basic theory of representations of finite groups of Lie type.
Author : Алексей Иванович Кострикин
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 48,7 Mb
Release : 1996
Category : Mathematics
ISBN : 3540570381
The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.
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 : 42,5 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.
