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Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
 
Martin W. Liebeck Imperial College of London, London, United Kingdom
Gary M. Seitz University of Oregon, Eugene, OR
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
Hardcover ISBN:  978-0-8218-6920-8
Product Code:  SURV/180
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-8510-9
Product Code:  SURV/180.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-6920-8
eBook: ISBN:  978-0-8218-8510-9
Product Code:  SURV/180.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
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Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
Martin W. Liebeck Imperial College of London, London, United Kingdom
Gary M. Seitz University of Oregon, Eugene, OR
Hardcover ISBN:  978-0-8218-6920-8
Product Code:  SURV/180
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-8510-9
Product Code:  SURV/180.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-6920-8
eBook ISBN:  978-0-8218-8510-9
Product Code:  SURV/180.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1802012; 380 pp
    MSC: Primary 20; 17;

    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.

    Readership

    Research mathematicians interested in algebraic groups.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1802012; 380 pp
MSC: Primary 20; 17;

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.

Readership

Research mathematicians interested in algebraic groups.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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