Unipotent And Nilpotent Classes In Simple Algebraic Groups And Lie Algebras
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Unipotent And Nilpotent Classes In Simple Algebraic Groups And Lie Algebras
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Author : Martin W. Liebeck
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-01-25
Unipotent And Nilpotent Classes In Simple Algebraic Groups And Lie Algebras written by Martin W. Liebeck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-25 with Mathematics categories.
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.
Centres Of Centralizers Of Unipotent Elements In Simple Algebraic Groups
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Author : Ross Lawther
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Centres Of Centralizers Of Unipotent Elements In Simple Algebraic Groups written by Ross Lawther and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Linear algebraic groups categories.
Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.
Algebraic Groups And Lie Groups With Few Factors
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Author : Alfonso Di Bartolo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-17
Algebraic Groups And Lie Groups With Few Factors written by Alfonso Di Bartolo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-17 with Mathematics categories.
This volume treats algebraic groups from a group theoretical point of view and compares the results with the analogous issues in the theory of Lie groups. It examines a classification of algebraic groups and Lie groups having only few subgroups.
Conjugacy Classes In Semisimple Algebraic Groups
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Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Conjugacy Classes In Semisimple Algebraic Groups written by James E. Humphreys and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Conjugacy classes categories.
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.
Unipotent Algebraic Groups
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Author : T. Kambayashi
language : en
Publisher: Springer
Release Date : 2006-11-15
Unipotent Algebraic Groups written by T. Kambayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Maximal Textrm Psl 2 Subgroups Of Exceptional Groups Of Lie Type
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Author : David A. Craven
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-08
Maximal Textrm Psl 2 Subgroups Of Exceptional Groups Of Lie Type written by David A. Craven and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.
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Nilpotent Orbits In Semisimple Lie Algebra
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Author : William.M. McGovern
language : en
Publisher: Routledge
Release Date : 2017-10-19
Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.
Conjugacy Classes In Algebraic Groups
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Author : R. Steinberg
language : en
Publisher: Springer
Release Date : 2006-11-15
Conjugacy Classes In Algebraic Groups written by R. Steinberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Representations Of Finite Groups Of Lie Type
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Author : François Digne
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-05
Representations Of Finite Groups Of Lie Type written by François Digne and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-05 with Mathematics categories.
An up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Simple Singularities And Simple Algebraic Groups
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Author : P. Slodowy
language : en
Publisher: Springer
Release Date : 2006-11-15
Simple Singularities And Simple Algebraic Groups written by P. Slodowy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.