Linear algebraic groups and finite groups of Lie type
著者
書誌事項
Linear algebraic groups and finite groups of Lie type
(Cambridge studies in advanced mathematics, 133)
Cambridge University Press, 2011
- : hardback
大学図書館所蔵 全46件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
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注記
"Grew out of a summer school on 'Finite Groups and Related Geometrical Structures' held in Venice from September 5th to September 15th 2007."--Pref
Includes bibliographical references (p. [301]-304) and index
内容説明・目次
内容説明
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
目次
- 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.
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