Linear algebraic groups and finite groups of lie type /
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| Author / Creator: | Malle, Gunter. |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, c2011. |
| Description: | xii, 309 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Cambridge studies in advanced mathematics ; 133 Cambridge studies in advanced mathematics ; 133. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8511207 |
Table of Contents:
- Preface
- List of tables
- Notation
- Part I. Linear Algebraic Groups
- 1. Basic concepts
- 2. Jordan decomposition
- 3. Commutative linear algebraic groups
- 4. Connected solvable groups
- 5. G-spaces and quotients
- 6. Borel subgroups
- 7. The Lie algebra of a linear algebraic group
- 8. Structure of reductive groups
- 9. The classification of semisimple algebraic groups
- 10. Exercises for Part I
- Part II. Subgroup Structure and Representation Theory of Semisimple Algebraic Groups
- 11. BN-pairs and Bruhat decomposition
- 12. Structure of parabolic subgroups, I
- 13. Subgroups of maximal rank
- 14. Centralizers and conjugacy classes
- 15. Representations of algebraic groups
- 16. Representation theory and maximal subgroups
- 17. Structure of parabolic subgroups, II
- 18. Maximal subgroups of classical type simple algebraic groups
- 19. Maximal subgroups of exceptional type algebraic groups
- 20. Exercises for Part II
- Part III. Finite Groups of Lie Type
- 21. Steinberg endomorphisms
- 22. Classification of finite groups of Lie type
- 23. Weyl group, root system and root subgroups
- 24. A BN-pair for GF
- 25. Tori and Sylow subgroups
- 26. Subgroups of maximal rank
- 27. Maximal subgroups of finite classical groups
- 28. About the classes CF1, ..., CF7 and S
- 29. Exceptional groups of Lie type
- 30. Exercises for Part III
- Appendix A. Root systems
- Appendix B. Subsystems
- Appendix C. Automorphisms of root systems
- References
- Index