Representations of Finite Groups of Lie Type

Representations of Finite Groups of Lie Type
Title Representations of Finite Groups of Lie Type PDF eBook
Author François Digne
Publisher Cambridge University Press
Pages 267
Release 2020-03-05
Genre 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.

The Character Theory of Finite Groups of Lie Type

The Character Theory of Finite Groups of Lie Type
Title The Character Theory of Finite Groups of Lie Type PDF eBook
Author Meinolf Geck
Publisher Cambridge University Press
Pages 406
Release 2020-02-27
Genre 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.

Linear Algebraic Groups and Finite Groups of Lie Type

Linear Algebraic Groups and Finite Groups of Lie Type
Title Linear Algebraic Groups and Finite Groups of Lie Type PDF eBook
Author Gunter Malle
Publisher Cambridge University Press
Pages 324
Release 2011-09-08
Genre 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.

Finite Groups of Lie Type

Finite Groups of Lie Type
Title Finite Groups of Lie Type PDF eBook
Author Roger W. Carter
Publisher
Pages 570
Release 1993-08-24
Genre 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.

Modular Representations of Finite Groups of Lie Type

Modular Representations of Finite Groups of Lie Type
Title Modular Representations of Finite Groups of Lie Type PDF eBook
Author James E. Humphreys
Publisher Cambridge University Press
Pages 260
Release 2006
Genre Mathematics
ISBN 9780521674546

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A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

Simple Groups of Lie Type

Simple Groups of Lie Type
Title Simple Groups of Lie Type PDF eBook
Author Roger W. Carter
Publisher John Wiley & Sons
Pages 350
Release 1989-01-18
Genre Mathematics
ISBN 9780471506836

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Now available in paperback--the standard introduction to the theory of simple groups of Lie type. In 1955, Chevalley showed how to construct analogues of the complex simple Lie groups over arbitrary fields. The present work presents the basic results in the structure theory of Chevalley groups and their twisted analogues. Carter looks at groups of automorphisms of Lie algebras, makes good use of Weyl group (also discussing Lie groups over finite fields), and develops the theory of Chevalley and Steinberg groups in the general context of groups with a (B,N)-pair. This new edition contains a corrected proof of the simplicity of twisted groups, a completed list of sporadic simple groups in the final chapter and a few smaller amendments; otherwise, this work remains the classic piece of exposition it was when it first appeared in 1971.

The Classification of the Finite Simple Groups, Number 3

The Classification of the Finite Simple Groups, Number 3
Title The Classification of the Finite Simple Groups, Number 3 PDF eBook
Author Daniel Gorenstein
Publisher American Mathematical Soc.
Pages 446
Release 1994
Genre Finite simple groups
ISBN 9780821803912

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Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR