Buch, Englisch, Band 126, 290 Seiten, Book, Format (B × H): 160 mm x 241 mm, Gewicht: 1350 g
Buch, Englisch, Band 126, 290 Seiten, Book, Format (B × H): 160 mm x 241 mm, Gewicht: 1350 g
Reihe: Graduate Texts in Mathematics
ISBN: 978-0-387-97370-8
Verlag: SPRINGER NATURE
Zielgruppe
Lower undergraduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.