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Hardcover ISBN:  9780821869208 
Product Code:  SURV/180 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9780821885109 
Product Code:  SURV/180.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821869208 
eBook ISBN:  9780821885109 
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 DetailsMathematical Surveys and MonographsVolume: 180; 2012; 380 ppMSC: 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.
ReadershipResearch 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. Nondistinguished unipotent classes

21. Proofs of theorems 1, 2 and corollaries 3–8

22. Tables of nilpotent and unipotent classes in the exceptional groups


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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.

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. Nondistinguished unipotent classes

21. Proofs of theorems 1, 2 and corollaries 3–8

22. Tables of nilpotent and unipotent classes in the exceptional groups