
Linear Algebraic Groups
Armand Borel(Author)
Springer (Publisher)
2nd Edition
Published on 30. September 2012
Book
Paperback/Softback
XI, 290 pages
978-1-4612-6954-0 (ISBN)
Description
This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally's structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.
More details
Product info
Paperback
Series
Band 126
Language
English
Place of publication
New York, NY
United States
Target group
Lower undergraduate
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 238 mm
Width: 154 mm
Thickness: 22 mm
Weight
462 gr
ISBN-13
978-1-4612-6954-0 (9781461269540)
DOI
10.1007/978-1-4612-0941-6
Schweitzer Classification
Other editions
Additional editions


Armand Borel
Linear Algebraic Groups
Book
04/1991
2nd Edition
Springer
€64.19
Article exhausted; check different version
Content
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.- 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.- II - Homogeneous Spaces.- §5. Semi-Invariants.- §6. Homogeneous Spaces.- §7. Algebraic Groups in Characteristic Zero.- III Solvable Groups.- §8. Diagonalizable Groups and Tori.- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements.- §10. Connected Solvable Groups.- IV-Borel Subgroups; Reductive Groups.- §11. Borel Subgroups.- §12. Cartan Subgroups; Regular Elements.- §13. The Borel Subgroups Containing a Given Torus.- §14. Root Systems and Bruhat Decomposition in Reductive Groups.- 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. Isotropic Reductive Groups.- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups.- §22. Central Isogenies.- §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.