Linear algebraic groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1991
|
| Ausgabe: | 2., enl. ed. |
| Schriftenreihe: | Graduate texts in mathematics
126 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 288 S. |
| ISBN: | 0387973702 3540973702 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear algebraic groups |c Armand Borel |
| 250 | |a 2., enl. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1991 | |
| 300 | |a X, 288 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction to the First Edition v
Introduction to the Second Edition vii
Conventions and Notation xi
Chapter AG—Background Material From Algebraic Geometry
§1. Some Topological Notions 1
§2. Some Facts from Field Theory 3
§3. Some Commutative Algebra 5
§4. Sheaves 10
§5. Affine K Schemes, Prevarieties 11
§6. Products; Varieties 14
§7. Projective and Complete Varieties 17
§8. Rational Functions; Dominant Morphisms 19
§9. Dimension 20
§10. Images and Fibres of a Morphism 20
§11. ^ structures on K Schemes 21
§12. /( Structures on Varieties 23
§13. Separable points 26
§14. Galois Criteria for Rationality 29
§15. Derivations and Differentials 32
§16. Tangent Spaces 36
§17. Simple Points 40
§18. Normal Varieties 42
References 45
Chapter I—General Notions Associated With Algebraic Groups
§1. The Notion of an Algebraic Groups 46
§2. Group Closure; Solvable and Nilpotent Groups 56
x Contents
§3. The Lie Algebra of an Algebraic Group 62
§4. Jordan Decomposition 79
Chapter 11—Homogeneous Spaces
§5. Semi Invariants 89
§6. Homogeneous Spaces 94
§7. Algebraic Groups in Characteristic Zero 105
Chapter III —Solvable Groups
§8. Diagonalizable Groups and Tori Ill
§9. Conjugacy Classes and Centralizers of
Semi Simple Elements 127
§10. Connected Solvable Groups 134
Chapter IV—Borel Subgroups; Reductive Groups
§11. Borel Subgroups 147
§12. Cartan Subgroups; Regular Elements 159
§13. The Borel Subgroups Containing a Given Torus 163
§14. Root Systems and Bruhat Decomposition
in Reductive Groups 179
Chapter V—Rationality Questions
§15. Split Solvable Groups and Subgroups 203
§16. Groups over Finite Fields 210
§17. Quotient of a Group by a Lie Subalgebra 213
§18. Cartan Subgroups over the Groundfield. Unirationality.
Splitting of Reductive Groups 218
§19. Cartan Subgroups of Solvable Groups 222
§20. Isotropic Reductive Groups 224
§21. Relative Root System and Bruhat Decomposition for
Isotropic Reductive Groups 229
§22. Central Isogenies 246
§23. Examples 253
§24. Survey of Some Other Topics 268
A. Classification 268
B. Linear Representations 270
C. Real Reductive Groups 274
References for Chapters I to V 280
Index of Definition 282
Index of Notation 286
|
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| discipline | Mathematik |
| edition | 2., enl. ed. |
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| indexdate | 2024-07-09T16:12:15Z |
| institution | BVB |
| isbn | 0387973702 3540973702 |
| language | English |
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| physical | X, 288 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Borel, Armand 1923-2003 Verfasser (DE-588)119089106 aut Linear algebraic groups Armand Borel 2., enl. ed. New York [u.a.] Springer 1991 X, 288 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 126 Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 s DE-604 Lineare algebraische Gruppe (DE-588)4295326-1 s Graduate texts in mathematics 126 (DE-604)BV000000067 126 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002720120&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borel, Armand 1923-2003 Linear algebraic groups Graduate texts in mathematics Lineare algebraische Gruppe (DE-588)4295326-1 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4295326-1 (DE-588)4001164-1 |
| title | Linear algebraic groups |
| title_auth | Linear algebraic groups |
| title_exact_search | Linear algebraic groups |
| title_full | Linear algebraic groups Armand Borel |
| title_fullStr | Linear algebraic groups Armand Borel |
| title_full_unstemmed | Linear algebraic groups Armand Borel |
| title_short | Linear algebraic groups |
| title_sort | linear algebraic groups |
| topic | Lineare algebraische Gruppe (DE-588)4295326-1 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Lineare algebraische Gruppe Algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002720120&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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