出版社:世界图书出版公司北京公司
年代:2009
定价:38.0
本书是一本数学专业的研究生教材。
Introduction to the First Edition
Introduction to the Second Edition
Conventions and Notation
CHAPTER AG--Background Material From Algebraic Geometry
1. Some Topological Notions
2. Some Facts from Field Theory
3. Some Commutative Algebra
4. Sheaves
5. Affine K-Schemes, Prevarieties
6. Products; Varieties
7. Projective and Complete Varieties
8. Rational Functions; Dominant Morphisms
9. Dimension
10. Images and Fibres of a Morphism
11. k-structures on K-Schemes
12. k-Structures on Varieties
13. Separable points
14. Galois Criteria for Rationality
15. Derivations and Differentials
16. Tangent Spaces
17. Simple Points
18. Normal Varieties
References
CHAPTER I--General Notions Associated With Algebraic Groups
1. The Notion of an Algebraic Groups
2. Group Closure; Solvable and Nilpotent Groups
3. The Lie Algebra of an Algebraic Group
4. Jordan Decomposition
CHAPTER 11 Homogeneous Spaces
5. Semi-lnvariants
6. Homogeneous Spaces
7. Algebraic Groups in Characteristic Zero
CHAPTER 111 Solvable Groups
8. Diagonalizable Groups and Tori
9. Conjugacy Classes and Centralizers of Scmi-Simple Elements
10. Connected Solvable Groups
CHAPTER IV -- Borel Subgroups; Rcductive Groups
11. Borei Subgroups
12. Caftan Subgroups; Regular Elements
13. The Borel Subgroups Containing a Given Torus
14. Root Systems and Bruhat Decomposition in Reductive Groups
CHAPTER V-- Rationality Questions
15. Split Solvable Groups and Subgroups
16. Groups over Finite Fields
17. Quotient of a Group by a Lie Subalgebra
18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups
19. Cartan Subgroups of Solvable Groups
20. lsotropic Reductive Groups
21. Relative Root System and Bruhat Decomposition for lsotropic ReductiveGroups
22. Central lsogenies
23. Examples
24. Survey of Some Other Topics
A. Classification
B. Linear Representations
C. Real Reductive Groups
References for Chapters I to V
Index of Definition
Index of Notation
Apart from some knowledge of Lie algebras, the main prerequisite for these Notes is some familiarity with algebraic geometry. In fact, comparatively little is actually needed. Most of the notions and results frequently used in the Notes are summarized, a few with proofs, in a preliminary Chapter AG. As a basic reference, we take Mumfords Notes [14], and have tried to be to some extent self-contained from there. A few further results from algebraic geometry needed on some specific occasions will be recalled (with references) where used. The point of view adopted here is essentially the set theoretic one: varieties are identified with their set of points over an algebraic closure of the groundfield (endowed with the Zariski-topology), however with some traces of the scheme point of view here and there.
书籍详细信息 | |||
书名 | 线性代数群站内查询相似图书 | ||
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出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
版次 | 2版 | 印次 | 1 |
定价(元) | 38.0 | 语种 | 英文 |
尺寸 | 14 | 装帧 | 平装 |
页数 | 印数 | 1000 |
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