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Unipotent and nilpotent classes in simple algebraic groups and Lie algebras

Author: M W Liebeck; Gary M Seitz
Publisher: Providence, Rhode Island : American Mathematical Society, [2012].
Series: Mathematical surveys and monographs, v. 180.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M W Liebeck; Gary M Seitz
ISBN: 9780821885109 0821885103
OCLC Number: 898200433
Description: 1 online resource (xii, 380 pages)
Contents: 1. Introduction 2. Preliminaries 3. Classical groups in good characteristic 4. Classical groups in bad characteristic: Statement of results 5. Nilpotent elements: The symplectic and orthogonal cases, $p=2$ 6. Unipotent elements in symplectic and orthogonal groups, $p=2$ 7. Finite classical groups 8. Tables of examples in low dimensions 9. Exceptional groups: Statement of results for nilpotent elements 10. Parabolic subgroups and labellings 11. Reductive subgroups 12. Annihilator spaces of nilpotent elements 13. Standard distinguished nilpotent elements 14. Exceptional distinguished nilpotent elements 15. Nilpotent classes and centralizers in $E_8$ 16. Nilpotent elements in the other exceptional types 17. Exceptional groups: Statement of results for unipotent elements 18. Corresponding unipotent and nilpotent elements 19. Distinguished unipotent elements 20. Non-distinguished unipotent classes 21. Proofs of theorems 1, 2 and corollaries 3-8 22. Tables of nilpotent and unipotent classes in the exceptional groups
Series Title: Mathematical surveys and monographs, v. 180.
Responsibility: Martin W. Liebeck, Gary M. Seitz

Abstract:

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.

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