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Books, Free Shipping, Linear Algebraic Groups

Posted at: Offers to Sell and Export | Posted on: Tue 27 Jul, 2010 7:10 am | Product Category: Algebra or pre algebra reference guides [21]
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Product Details

Author A.Borel

Publisher World Publishing Corporation

Isbn 9787510004810, 7510004810


August 2009

Pages 288

Size 24k

Edition First

Format Paperback

Language English

Page material gelatine plate paper

Product Description:

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 Mumford's 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.


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


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

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