Representation theory of Artin algebras:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 423 S. |
| ISBN: | 0521411343 |
Internformat
MARC
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| 245 | 1 | 0 | |a Representation theory of Artin algebras |c Maurice Auslander, Idun Reiten and Sverre O. Smalø |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XIV, 423 S. | ||
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Datensatz im Suchindex
| _version_ | 1804124401186111488 |
|---|---|
| adam_text | Contents
Introduction pagexi
I Artin rings 1
1 Finite length modules 1
2 Right and left minimal morphisms 6
3 Radical of rings and modules 8
4 Structure of projective modules 12
5 Some homological facts 16
Exercises 23
Notes 25
II Artin algebras 26
1 Artin algebras and categories 26
2 Projectivization 32
3 Duality 37
4 Structure of injective modules 39
5 Blocks 43
Exercises 45
Notes 47
III Examples of algebras and modules 49
1 Quivers and their representations 49
2 Triangular matrix rings 70
3 Group algebras 79
4 Skew group algebras 83
Excercises 94
Notes 99
IV The transpose and the dual 100
1 The transpose 100
2 Nakayama algebras 111
3 Selfinjective algebras 122
vii
viii Contents
4 Defect of exact sequences 128
Exercises 133
Notes 135
V Almost split sequences 136
1 Almost split sequences and morphisms 136
2 Interpretation and examples 147
3 Projective or injective middle terms 153
4 Group algebras 158
5 Irreducible morphisms 166
6 The middle term 173
7 The radical 178
Exercises 185
Notes 189
VI Finite representation type 191
1 A criterion 191
2 Nakayama algebras 197
3 Group algebras 200
4 Grothendieck groups 206
5 Auslander algebras 209
Exercises 219
Notes 221
VII The AusIander Reiten quiver 224
1 The Auslander Reiten quiver 224
2 Auslander Reiten quivers and finite type 232
3 Cartan matrices 241
4 Translation quivers 248
Exercises 253
Notes 256
VIII Hereditary algebras 257
1 Preprojective and preinjective modules 258
2 The Coxeter transformation 269
3 The homological quadratic form 272
4 Regular components 277
5 Finite representation type 288
6 Quadratic forms and roots 294
7 Kronecker algebras 302
Exercises 309
Notes 311
IX Short chains and cycles 313
1 Short cycles 313
Contents ix
2 Modules determined by composition factors 320
3 Sincere modules and short cycles 323
4 Modules determined by their top and socle 326
Exercises 332
Notes 333
X Stable equivalence 335
1 Stable equivalence and almost split sequences 335
2 Artin algebras with radical square zero 344
3 Symmetric Nakayama algebras 352
Exercises 362
Notes 364
XI Modules determining morphisms 365
1 Morphisms determined by a module 365
2 Modules determining a morphism 370
3 Classification of morphisms 379
4 Rigid exact sequences 385
5 Indecomposable middle terms 389
Exercises 399
Notes 405
Notation 406
Conjectures 409
Open problems 411
Bibliography 413
Relevant conference proceedings 420
Index 421
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:04Z |
| institution | BVB |
| isbn | 0521411343 |
| language | English |
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| physical | XIV, 423 S. |
| publishDate | 1995 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Auslander, Maurice Verfasser aut Representation theory of Artin algebras Maurice Auslander, Idun Reiten and Sverre O. Smalø 1. publ. Cambridge u.a. Cambridge Univ. Press 1995 XIV, 423 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 36 Anneaux artiniens ram Representatie (wiskunde) gtt Représentations d'algèbre ram Ringen (wiskunde) gtt Artin algebras Artin rings Representations of algebras Artinsche Algebra (DE-588)4143137-6 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Artinsche Algebra (DE-588)4143137-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Reiten, Idun 1942- Verfasser (DE-588)108418413 aut Smalø, Sverre O. Verfasser aut Cambridge studies in advanced mathematics 36 (DE-604)BV000003678 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006644372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Auslander, Maurice Reiten, Idun 1942- Smalø, Sverre O. Representation theory of Artin algebras Cambridge studies in advanced mathematics Anneaux artiniens ram Representatie (wiskunde) gtt Représentations d'algèbre ram Ringen (wiskunde) gtt Artin algebras Artin rings Representations of algebras Artinsche Algebra (DE-588)4143137-6 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4143137-6 (DE-588)4148816-7 |
| title | Representation theory of Artin algebras |
| title_auth | Representation theory of Artin algebras |
| title_exact_search | Representation theory of Artin algebras |
| title_full | Representation theory of Artin algebras Maurice Auslander, Idun Reiten and Sverre O. Smalø |
| title_fullStr | Representation theory of Artin algebras Maurice Auslander, Idun Reiten and Sverre O. Smalø |
| title_full_unstemmed | Representation theory of Artin algebras Maurice Auslander, Idun Reiten and Sverre O. Smalø |
| title_short | Representation theory of Artin algebras |
| title_sort | representation theory of artin algebras |
| topic | Anneaux artiniens ram Representatie (wiskunde) gtt Représentations d'algèbre ram Ringen (wiskunde) gtt Artin algebras Artin rings Representations of algebras Artinsche Algebra (DE-588)4143137-6 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Anneaux artiniens Representatie (wiskunde) Représentations d'algèbre Ringen (wiskunde) Artin algebras Artin rings Representations of algebras Artinsche Algebra Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006644372&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
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