Linear algebraic groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1998
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Progress in mathematics
9 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008291425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 334 S. |
| ISBN: | 3764340215 0817640215 |
Internformat
MARC
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| 100 | 1 | |a Springer, Tonny A. |d 1926- |e Verfasser |0 (DE-588)115799729 |4 aut | |
| 245 | 1 | 0 | |a Linear algebraic groups |c T. A. Springer |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a X, 334 S. | ||
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| 490 | 1 | |a Progress in mathematics |v 9 | |
| 650 | 7 | |a Algebraïsche groepen |2 gtt | |
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Datensatz im Suchindex
| _version_ | 1819373240350408704 |
|---|---|
| adam_text | Contents
Preface to the Second Edition xi
1. Some Algebraic Geometry 1
1.1. The Zariski topology 1
1.2. Irreducibility of topological spaces 2
1.3. Affine algebras 4
1.4. Regular functions, ringed spaces 6
1.5. Products 10
1.6. Prevarieties and varieties 11
1.7. Projective varieties 14
1.8. Dimension 16
1.9. Some results on morphisms 17
Notes 20
2. Linear Algebraic Groups, First Properties 21
2.1. Algebraic groups 21
2.2. Some basic results 25
2.3. G spaces 28
2.4. Jordan decomposition 31
2.5. Recovering a group from its representations 37
Notes 41
3. Commutative Algebraic Groups 42
3.1. Structure of commutative algebraic groups 42
3.2. Diagonalizable groups and tori 43
vi Contents
3.3. Additive functions 49
3.4. Elementary unipotent groups 51
Notes 56
4. Derivations, Differentials, Lie Algebras 57
4.1. Derivations and tangent spaces 57
4.2. Differentials, separability 60
4.3. Simple points 66
4.4. The Lie algebra of a linear algebraic group 69
Notes 77
5. Topological Properties of Morphisms, Applications 78
5.1. Topological properties of morphisms 78
5.2. Finite morphisms, normality 82
5.3. Homogeneous spaces 86
5.4. Semi simple automorphisms 88
5.5. Quotients 91
Notes 97
6. Parabolic Subgroups, Borel Subgroups, Solvable Groups 98
6.1. Complete varieties 98
6.2. Parabolic subgroups and Borel subgroups 101
6.3. Connected solvable groups 104
6.4. Maximal tori, further properties of Borel groups 108
Notes 113
Contents vii
7. Weyl Group, Roots, Root Datum 114
7.1. The Weyl group 114
7.2. Semi simple groups of rank one 117
7.3. Reductive groups of semi simple rank one 120
7.4. Root data 124
7.5. Two roots 128
7.6. The unipotent radical 130
Notes 131
8. Reductive Groups 132
8.1. Structural properties of areductive group 132
8.2. Borel subgroups and systems of positive roots 137
8.3. The Bruhat decomposition 142
8.4. Parabolic subgroups 146
8.5. Geometric questions related to the Bruhat decomposition 149
Notes 153
9. The Isomorphism Theorem 154
9.1. Two dimensional root systems 154
9.2. The structure constants 156
9.3. The elements na 162
9.4. A presentation of G 164
9.5. Uniqueness of structure constants 168
9.6. The isomorphism theorem 170
Notes 174
viii Contents
10. The Existence Theorem 175
10.1. Statement of the theorem, reduction 175
10.2. Simply laced root systems 177
10.3. Automorphisms, end of the proof of 10.1.1 181
Notes 184
11. More Algebraic Geometry 185
11.1. F structures on vector spaces 185
11.2. F varieties: density, criteria for ground fields 191
11.3. Forms 196
11.4. Restriction of the ground field 198
Notes 207
12. F groups: General Results 208
12.1. Field of definition of subgroups 208
12.2. Complements on quotients 212
12.3. Galois cohomology 216
12.4. Restriction of the ground field 220
Notes 222
13. F tori 223
13.1. Diagonalizable groups over F 223
13.2. F tori 225
13.3. Tori in F groups 227
13.4. The groups P(k) 233
Notes 236
Contents ix
14. Solvable F groups 237
14.1. Generalities 237
14.2. Action of Gfl on an affine variety, applications 239
14.3. F split solvable groups 243
14.4. Structural properties of solvable groups 248
Notes 251
15. F reductive Groups 252
15.1. Pseudo parabolic F subgroups 252
15.2. A fixed point theorem 254
15.3. The root datum of an F reductive group 256
15.4. The groups C/(a) 262
15.5. The index 265
Notes 268
16. Reductive F groups 269
16.1. Parabolic subgroups 269
16.2. Indexed root data 271
16.3. F split groups 274
16.4. The isomorphism theorem 278
16.5. Existence 281
Notes 284
17. Classification 285
17.1. Type AB_i 285
x Contents
17.2. Types Bn and Cn 289
17.3. Type Dn 293
17.4. Exceptional groups, type G2 300
17.5. Indices for types F4 and E 302
17.6. Descriptions for type F4 305
17.7. Type E6 310
17.8. Type £7 312
17.9. Trialitarian type D4 315
17.10. Special fields 317
Notes 319
Table of Indices 320
Bibliography 323
Index 331
|
| any_adam_object | 1 |
| author | Springer, Tonny A. 1926- |
| author_GND | (DE-588)115799729 |
| author_facet | Springer, Tonny A. 1926- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 21 512/.55 |
| dewey-search | 512/.55 21 512/.55 |
| dewey-sort | 3512 255 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV012236917 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:26:46Z |
| institution | BVB |
| isbn | 3764340215 0817640215 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008291425 |
| oclc_num | 38179868 |
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| physical | X, 334 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Springer, Tonny A. 1926- Linear algebraic groups Progress in mathematics Algebraïsche groepen gtt Linear algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| subject_GND | (DE-588)4001164-1 (DE-588)4001161-6 (DE-588)4295326-1 |
| title | Linear algebraic groups |
| title_auth | Linear algebraic groups |
| title_exact_search | Linear algebraic groups |
| title_full | Linear algebraic groups T. A. Springer |
| title_fullStr | Linear algebraic groups T. A. Springer |
| title_full_unstemmed | Linear algebraic groups T. A. Springer |
| title_short | Linear algebraic groups |
| title_sort | linear algebraic groups |
| topic | Algebraïsche groepen gtt Linear algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| topic_facet | Algebraïsche groepen Linear algebraic groups Algebraische Gruppe Algebraische Geometrie Lineare algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008291425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT springertonnya linearalgebraicgroups |