Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Martin W. Liebeck, Gary M. Seitz

ISBN 10: 0821869205 / ISBN 13: 9780821869208

Published by American Mathematical Society, US, 2012

About this Item

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.

Seller Inventory # LU-9780821869208

Bibliographic Details

• Title: Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
• Publisher: American Mathematical Society, US
• Publication Date: 2012
• Language: English
• ISBN 10: 0821869205
• ISBN 13: 9780821869208
• Binding: Hardback
• Condition: New
• Weight: 840 grams

About this title

Synopsis

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.