A 1 Subgroups Of Exceptional Algebraic Groups

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A 1 Subgroups Of Exceptional Algebraic Groups

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Author : Ross Lawther
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

A 1 Subgroups Of Exceptional 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 1999 with Mathematics categories.

This book is intended for graduate students and research mathematicians interested in group theory and genralizations

The Irreducible Subgroups Of Exceptional Algebraic Groups

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Author : Adam R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

The Irreducible Subgroups Of Exceptional Algebraic Groups written by Adam R. Thomas 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 2021-06-18 with Education categories.

This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.

Reductive Subgroups Of Exceptional Algebraic Groups

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Author : Martin W. Liebeck
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Reductive Subgroups Of Exceptional Algebraic Groups 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 1996 with Mathematics categories.

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.

Maximal Subgroups Of Exceptional Algebraic Groups

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Author : Gary M. Seitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Maximal Subgroups Of Exceptional Algebraic Groups written by Gary M. Seitz 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 1991 with Mathematics categories.

Let [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.

A Subgroups Of Exceptional Algebraic Groups

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Author : Ross Lawther
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11

A Subgroups Of Exceptional Algebraic Groups written by Ross Lawther and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Lie algebras categories.

This book is intended for graduate students and research mathematicians interested in group theory and genralizations

Algebraic Groups And Their Representations

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Author : R.W. Carter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebraic Groups And Their Representations written by R.W. Carter 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 2012-12-06 with Mathematics categories.

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.

Linear Algebraic Groups And Finite Groups Of Lie Type

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Author : Gunter Malle
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08

Linear Algebraic Groups And Finite Groups Of Lie Type written by Gunter Malle 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 2011-09-08 with Mathematics categories.

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.

The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups

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Author : Martin W. Liebeck
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups 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 2004 with Mathematics categories.

Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.

Groups Combinatorics Geometry

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Author : A. A. Ivanov
language : en
Publisher: World Scientific
Release Date : 2003

Groups Combinatorics Geometry written by A. A. Ivanov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

"This book contains the proceedings of the L.M.S. Durham Symposium on Groups, Geometry and Combinatorics, July 16-26, 2001"--P. v.

Representations Of Reductive Groups

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Author : Roger W. Carter
language : en
Publisher: Cambridge University Press
Release Date : 1998-09-03

Representations Of Reductive Groups written by Roger W. Carter 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 1998-09-03 with Mathematics categories.

This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.