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Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
Martin W. Liebeck, Imperial College of London, United Kingdom, and Gary M. Seitz, University of Oregon, Eugene, OR

Mathematical Surveys and Monographs
2012; 380 pp; hardcover
Volume: 180
ISBN-10: 0-8218-6920-5
ISBN-13: 978-0-8218-6920-8
List Price: US$96
Member Price: US$76.80
Order Code: SURV/180
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See also:

Algebras, Rings and Modules: Lie Algebras and Hopf Algebras - Michiel Hazewinkel, Nadiya Gubareni and V V Kirichenko

The Classification of Finite Simple Groups: Groups of Characteristic 2 Type - Michael Aschbacher, Richard Lyons, Stephen D Smith and Ronald Solomon

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.


Research mathematicians interested in algebraic groups.

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