[PDF] Conjugacy Classes And Centralizers Of Semisimple Elements In Finite Groups Of Lie Type eBook

Author : James E. Humphreys
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 25,19 MB
Release : 1995
Category : Education
ISBN : 0821852760

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Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

Author : François Digne
Publisher : Cambridge University Press
Page : 267 pages
File Size : 44,4 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 : Gunter Malle
Publisher : Cambridge University Press
Page : 324 pages
File Size : 11,62 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 : Meinolf Geck
Publisher : Cambridge University Press
Page : 405 pages
File Size : 18,58 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 : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 30,11 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 0821869205

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This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.