[PDF] Conjugacy Classes Of Non Connected Semisimple Algebraic Groups eBook

Author : James E. Humphreys
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 30,79 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 : Thomas W. Cusick
Publisher : American Mathematical Soc.
Page : 109 pages
File Size : 22,17 MB
Release : 1989
Category : Mathematics
ISBN : 0821815318

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This book is directed at mathematicians interested in Diophantine approximation and the theory of quadratic forms and the relationship of these subjects to Markoff and Lagrange spectra. The authors have gathered and systemized numerous results from the diverse and scattered literature, much of which has appeared in rather inaccessible Russian publications. Readers will find a comprehensive overview of the theory of the Markoff and Lagrange spectra, starting with the origins of the subject in two papers of A. Markoff from 1879-80. Most of the progress since that time has occurred in the last 20 years or so, when there has been a resurgence of interest in these spectra. The authors provide an excellent exposition of these developments, in addition to presenting many proofs and correcting various errors in the literature.

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 43,60 MB
Release : 1996
Category : Mathematics
ISBN : 0821804618

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The theory of simple algebraic groups is important in many areas of mathematics. The authors of this book investigate the subgroups of certain types of simple algebraic groups and obtain a complete description of all those subgroups which are themselves simple. This description is particularly useful in understanding centralizers of subgroups and restrictions of representations.

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 24,10 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.

Author : Roger W. Carter
Publisher :
Page : 570 pages
File Size : 40,60 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.