Unipotent and nilpotent classes in simple algebraic groups and Lie algebras / Martin W. Liebeck, Gary M. Seitz.

Format:

Book

Author/Creator:

Liebeck, M. W. (Martin W.), 1954- author.

Seitz, Gary M., 1943- author.

Series:

Mathematical surveys and monographs ; Volume 180.

Mathematical surveys and monographs ; Volume 180

Language:

English

Subjects (All):

Linear algebraic groups.

Lie algebras.

Physical Description:

1 online resource (xii, 380 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

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.

Contents:

Cover

Title page

Contents

Preface

Introduction

Preliminaries

Classical groups in good characteristic

Classical groups in bad characteristic: Statement of results

Nilpotent elements: The symplectic and orthogonal cases, =2

Unipotent elements in symplectic and orthogonal groups, =2

Finite classical groups

Tables of examples in low dimensions

Exceptional groups: Statement of results for nilpotent elements

Parabolic subgroups and labellings

Reductive subgroups

Annihilator spaces of nilpotent elements

Standard distinguished nilpotent elements

Exceptional distinguished nilpotent elements

Nilpotent classes and centralizers in ₈

Nilpotent elements in the other exceptional types

Exceptional groups: Statement of results for unipotent elements

Corresponding unipotent and nilpotent elements

Distinguished unipotent elements

Non-distinguished unipotent classes

Proofs of theorems 1, 2 and corollaries 3-8

Tables of nilpotent and unipotent classes in the exceptional groups

Bibliography

Glossary of symbols

Index

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (pages 373-375) and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-8218-8510-3

OCLC:

898200433