[PDF] Linear Algebraic Groups And Finite Groups Of Lie Type eBook

Author : Gunter Malle
Publisher : Cambridge University Press
Page : 324 pages
File Size : 11,91 MB
Release : 2011-09-08
Category : Mathematics
ISBN : 113949953X

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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 : Gunter Malle
Publisher :
Page : 325 pages
File Size : 44,34 MB
Release : 2011
Category : Electronic books
ISBN : 9781139123600

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The first textbook on the subgroup structure, in particular maximal subgroups, for both algebraic and finite groups of Lie type.

Author : François Digne
Publisher : Cambridge University Press
Page : 267 pages
File Size : 21,1 MB
Release : 2020-03-05
Category : Mathematics
ISBN : 1108481485

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An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.

Author : Meinolf Geck
Publisher : Cambridge University Press
Page : 406 pages
File Size : 44,24 MB
Release : 2020-02-27
Category : Mathematics
ISBN : 1108808905

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Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 46,8 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X

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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 : Peter Schneider
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 30,45 MB
Release : 2011-06-11
Category : Mathematics
ISBN : 364221147X

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Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Author : R.W. Carter
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 48,94 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401153086

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This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.

Author : Meinolf Geck
Publisher : Cambridge University Press
Page : 405 pages
File Size : 11,83 MB
Release : 2020-02-27
Category : Mathematics
ISBN : 1108489621

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A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.

Author : Roger W. Carter
Publisher :
Page : 570 pages
File Size : 37,97 MB
Release : 1993-08-24
Category : Mathematics
ISBN :

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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.