Frobenius Algebras: 1 Basic representation theory
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Society
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 650 Seiten |
| ISBN: | 9783037191026 |
Internformat
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Datensatz im Suchindex
| _version_ | 1814902693966118912 |
|---|---|
| adam_text |
Titel: Bd. 1. Frobenius algebras. Basic representation theory
Autor: Skowroński, Andrzej
Jahr: 2011
Contents
Introduction ix
I Algebras and modules 1
1 Algebras. 1
2 Representations of algebras and modules . 12
3 The Jacobson radical. 30
4 The Krull-Schmidt theorem. 41
5 Semisimple modules. 45
6 Semisimple algebras. 56
7 The Jordan-Holder theorem. 67
8 Projective and injective modules. 73
9 Hereditary algebras. 93
10 Nakayama algebras. 100
11 The Grothendieck group and the Cartan matrix. 105
12 Exercises. 109
II Monta theory 123
1 Categories and functors. 123
2 Bimodules. 125
3 Tensor products of modules . 133
4 Adjunctions and natural isomorphisms. 140
5 Progenerators. 151
6 Morita equivalence. 157
7 Morita-Azumaya duality. 175
8 Exercises. 188
III Auslander-Reiten theory 203
1 The radical of a module category. 203
2 The Harada-Sai lemma. 207
3 The space of extensions. 209
4 The Auslander-Reiten translations. 232
5 The Nakayama functors. 247
6 The Auslander-Reiten formulas. 252
7 Irreducible and almost split homomorphisms . 257
8 Almost split sequences. 269
9 The Auslander-Reiten quiver. 282
10 The Auslander theorem. 301
viii Contents
11 The Bautista-Smal0 theorem. 312
12 Exercises. 314
IV Selfinjective algebras 332
1 The Frobenius theorem. 332
2 The Brauer-Nesbitt-Nakayama theorems. 336
3 Frobenius algebras. 345
4 Symmetric algebras. 355
5 Simple algebras. 368
6 The Nakayama theorems. 375
7 Non-Frobenius selfinjective algebras. 386
8 The syzygy functors . 392
9 The higher extension spaces. 402
10 Periodic modules. 414
11 Periodic algebras. 427
12 The Green-Snashall-Solberg theorems . 442
13 Dynkin and Euclidean graphs . 447
14 Canonical mesh algebras of Dynkin type. 452
15 The Riedtmann-Todorov theorem. 455
16 Exercises. 470
V Hecke algebras 489
1 Finite reflection groups. 489
2 Coxeter graphs. 499
3 The Coxeter theorems . 507
4 The Iwahori theorem. 515
5 Hecke algebras. 528
6 Exercises. 533
VI Hopf algebras 539
1 Coalgebras. 539
2 Hopfalgebras. 552
3 The Larson-Sweedler theorems . 584
4 The Radford theorem. 595
5 The Fischman-Montgomery-Schneider formula. 609
6 The module category. 616
7 Exercises. 630
Bibliography 637
Index 645 |
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| id | DE-604.BV042009168 |
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| indexdate | 2024-11-05T17:01:25Z |
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| isbn | 9783037191026 |
| language | English |
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| physical | XI, 650 Seiten |
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| spelling | Skowroński, Andrzej 1950- Verfasser (DE-588)141208694 aut Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata Zürich European Mathematical Society 2011 XI, 650 Seiten txt rdacontent n rdamedia nc rdacarrier Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hecke-Algebra (DE-588)4159341-8 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 s Hecke-Algebra (DE-588)4159341-8 s Hopf-Algebra (DE-588)4160646-2 s DE-604 Yamagata, Kunio Verfasser (DE-588)1022466070 aut (DE-604)BV042009165 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027451058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skowroński, Andrzej 1950- Yamagata, Kunio Frobenius Algebras Hopf-Algebra (DE-588)4160646-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd Frobenius-Algebra (DE-588)4155476-0 gnd |
| subject_GND | (DE-588)4160646-2 (DE-588)4159341-8 (DE-588)4155476-0 |
| title | Frobenius Algebras |
| title_auth | Frobenius Algebras |
| title_exact_search | Frobenius Algebras |
| title_full | Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata |
| title_fullStr | Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata |
| title_full_unstemmed | Frobenius Algebras 1 Basic representation theory Andrzej Skowroński, Kunio Yamagata |
| title_short | Frobenius Algebras |
| title_sort | frobenius algebras basic representation theory |
| topic | Hopf-Algebra (DE-588)4160646-2 gnd Hecke-Algebra (DE-588)4159341-8 gnd Frobenius-Algebra (DE-588)4155476-0 gnd |
| topic_facet | Hopf-Algebra Hecke-Algebra Frobenius-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027451058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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