Frobenius Algebras II

Tilted and Hochschild Extension Algebras

  • Andrzej Skowroński

    Nicolaus Copernicus University, Toruń, Poland
  • Kunio Yamagata

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