A Subgroups Of Exceptional Algebraic Groups

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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.

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.

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

Irreducible Subgroups Of Exceptional Algebraic Groups

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Author : Donna M. Testerman
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Irreducible Subgroups Of Exceptional Algebraic Groups written by Donna M. Testerman 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 1988 with Mathematics categories.

Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.

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.

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups

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Author : Alastair J. Litterick
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups written by Alastair J. Litterick 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 2018-05-29 with Mathematics categories.

The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.

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.

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

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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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.