Frobenius Algebras II
Tilted and Hochschild Extension Algebras
Andrzej Skowroński
Nicolaus Copernicus University, Toruń, PolandKunio Yamagata
Tokyo University of Agriculture and Technology, Japan
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| FrontmatterDownload pp. i–v | |
| ContentsDownload pp. vii–viii | |
| IntroductionDownload pp. ix–x | |
| Chapter VII Hereditary algebraspp. 1–2 | |
| 1 | The quiver of an algebrapp. 2–19 |
| 2 | The tensor algebras of speciespp. 19–29 |
| 3 | The tensor algebras of speciespp. 29–53 |
| 4 | The Euler formspp. 53–75 |
| 5 | The Coxeter transformationpp. 75–82 |
| 6 | Postprojective and preinjective componentspp. 82–96 |
| 7 | Hereditary algebras of Dynkin typepp. 96–111 |
| 8 | Hereditary algebras of Euclidean typepp. 111–158 |
| 9 | Hereditary algebras of wild typepp. 158–196 |
| 10 | Representations of bimodulespp. 197–205 |
| 11 | Exercisespp. 205–215 |
| Chapter VIII Tilted algebrasp. 217 | |
| 1 | Torsion pairspp. 218–225 |
| 2 | Tilting modulespp. 225–242 |
| 3 | The Brenner–Butler theorempp. 242–284 |
| 4 | Connecting sequencespp. 284–294 |
| 5 | Splitting tilting modulespp. 294–301 |
| 6 | Tilted algebraspp. 301–346 |
| 7 | The criterion of Liu and Skowrońskipp. 346–361 |
| 8 | Reflections of hereditary algebraspp. 362–367 |
| 9 | The theorem of Ringel on regular tilting modulespp. 367–385 |
| 10 | Exercisespp. 385–405 |
| Chapter IX Auslander–Reiten componentsp. 407 | |
| 1 | Functors on module categoriespp. 407–422 |
| 2 | The Igusa–Todorov theorempp. 422–428 |
| 3 | Degrees of irreducible homomorphismspp. 428–442 |
| 4 | Stable Auslander–Reiten componentspp. 442–453 |
| 5 | Generalized standard Auslander–Reiten componentspp. 453–456 |
| 6 | Stable equivalencepp. 456–469 |
| 7 | Exercisespp. 469–475 |
| Chapter X Selfinjective Hochschild extension algebrasp. 477 | |
| 1 | Hochschild cohomology spacespp. 477–478 |
| 2 | Hochschild extension algebraspp. 479–487 |
| 3 | Hochschild extensions by duality modulespp. 488–505 |
| 4 | Non-Frobenius selfinjective Hochschild extensionspp. 505–517 |
| 5 | Hochschild extension algebras of finite field extensionspp. 517–529 |
| 6 | Hochschild extension algebras of path algebraspp. 529–540 |
| 7 | Hochschild extension algebras of hereditary algebraspp. 540–553 |
| 8 | The Auslander–Reiten quivers of Hochschild extension algebraspp. 553–600 |
| 9 | Exercisespp. 601–610 |
| Bibliographypp. 611–615 | |
| Indexpp. 617–619 |