Author | Borel, Armand. author |
---|---|
Title | Linear Algebraic Groups [electronic resource] / by Armand Borel |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1991 |
Edition | Second Enlarged Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0941-6 |
Descript | XI, 290 p. online resource |
AGโBackground Material From Algebraic Geometry -- ยง1. Some Topological Notions -- ยง2. Some Facts from Field Theory -- ยง3. Some Commutative Algebra -- ยง4. Sheaves -- ยง5. Affine K-Schemes, Prevarieties -- ยง6. Products; Varieties -- ยง7. Projective and Complete Varieties -- ยง8. Rational Functions; Dominant Morphisms -- ยง9. Dimension -- ยง10. Images and Fibres of a Morphism -- ยง11. k-structures on K-Schemes -- ยง12. k-Structures on Varieties -- ยง13. Separable points -- ยง14. Galois Criteria for Rationality -- ยง15. Derivations and Differentials -- ยง16. Tangent Spaces -- ยง17. Simple Points -- ยง18. Normal Varieties -- References -- IโGeneral Notions Associated With Algebraic Groups -- ยง1. The Notion of an Algebraic Groups -- ยง2. Group Closure; Solvable and Nilpotent Groups -- ยง3. The Lie Algebra of an Algebraic Group -- ยง4. Jordan Decomposition -- II โ Homogeneous Spaces -- ยง5. Semi-Invariants -- ยง6. Homogeneous Spaces -- ยง7. Algebraic Groups in Characteristic Zero -- III Solvable Groups -- ยง8. Diagonalizable Groups and Tori -- ยง9. Conjugacy Classes and Centralizers of Semi-Simple Elements -- ยง10. Connected Solvable Groups -- IVโBorel Subgroups; Reductive Groups -- ยง11. Borel Subgroups -- ยง12. Cartan Subgroups; Regular Elements -- ยง13. The Borel Subgroups Containing a Given Torus -- ยง14. Root Systems and Bruhat Decomposition in Reductive Groups -- VโRationality Questions -- ยง15. Split Solvable Groups and Subgroups -- ยง16. Groups over Finite Fields -- ยง17. Quotient of a Group by a Lie Subalgebra -- ยง18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups -- ยง19. Cartan Subgroups of Solvable Groups -- ยง20. Isotropic Reductive Groups -- ยง21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups -- ยง22. Central Isogenies -- ยง23. Examples -- ยง24. 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