Deformed preprojective algebras of generalized dynkin type

Transactions of the American Mathematical Society

Volumn 359, Issue 6, 2007, Pages 2625-2650

  Białkowski, Jerzy ^a   Erdmann, Karin ^b   Skowroński, Andrzej ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 57649164231     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-03948-7     Document Type: Article

References (28)

1. M. Artin, Maximal orders of global dimension and Krull dimension two, Invent. Math. 84 (1986), 195-222. MR0830045 (88e:16008a)
2. M. Auslander, I. Reiten, Almost split sequences for rational double points, Trans. Amer. Math. Soc. 302 (1987), 87-97. MR0887498 (88e:13011)
3. M. Auslander, I. Reiten, D Tr-periodic modules and functors, in: Representation Theory of Algebras, CMS Conference Proceedings, Vol. 18, Amer. Math. Soc., Providence, RI, 1996, pp. 39-50. MR1388043 (98g:16008)
4. M. Auslander, I. Reiten, S.O. Smalo, Representation Theory of Artin Algebras, in: Cambridge Studies in Advanced Mathematics, Vol. 36, Cambridge University Press, Cambridge, UK, 1995. MR1314422 (96c:16015)
5. D. Baer, W. Geigle, H. Lenzing, The preprojective algebra of a tame hereditary Artin algebra, Comm. Algebra 15 (1987), 425-457. MR0876985 (88i:16036)
6. J. Bialkowski, A. Skowrohski, Selfinjective algebras of tubular type, Colloq. Math. 94 (2002), 175-194. MR1967373 (2004a:16019)
7. J. Bialkowski, A. Skowrohski, On tame weakly symmetric algebras of tubular type, Archiv Math. 81 (2003), 142-154. MR2009556 (2004k:16039)
8. J. Bialkowski, A. Skowrohski, Socle deformations of selfinjective algebras of tubular type, J. Math. Soc. Japa 56 (2004) 3, 687-716. MR2071668 (2005c:16018)
9. R.O. Buchweitz, Finite representation type and periodic Hochschild (co-)homology, in: Trends in the Representation Theory of Finite Dimensional Algebras, Contemp. Math., Vol. 229, Amer. Math. Soc., Providence, RI, 1998, pp. 81-109. MR1676212 (2000b:18001)
10. W. Crawley-Boevey, M.P. Holland, Noncommutative deformations ofKleinian singularities, Duke Math. J. 92 (1998), 605-635. MR1620538 (99f:14003)
11. V. Dlab, C.M. Ringel, The preprojective algebra ofa modulated graph, in: Representation Theory II, in: Lecture Notes in Math., Vol. 832, Springer-Verlag, Berlin/New York, 1980, pp. 216-231. MR0607155 (83c:16022)
12. V. Dlab, C.M. Ringel, The module theoretical approach to quasi-hereditary algebras, in: Representations of Algebras and Related Topics, in: London Mathematical Society Lecture Note Series, Vol. 168, Cambridge University Press, Cambridge, UK, 1992, pp. 200-224. MR1211481 (94f:16026)
13. K. Erdmann, N. Snashall, On Hochschild cohomology of preprojective algebras I, J. Algebra 205 (1998), 391-412. MR1632808 (99e:16013)
14. K. Erdmann, N. Snashall, Preprojective algebras ofDynkin type, periodicity and the second Hochschild cohomology, in: Algebras and Modules II, CMS Conference Proceedings, Vol. 24, Amer. Math. Soc., Providence, RI, 1998, pp. 183-193. MR1648626 (99h:16016)
15. P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Repre-sentation Theory I, in: Lecture Notes in Math., Vol. 831, Springer-Verlag, Berlin/New York, 1980, pp. 1-71. MR0607140 (82i:16030)
16. E.L. Green, N. Snashall, O. Solberg, The Hochschild cohomology ring of a selfinjective algebra of finite representation type, Proc. Amer. Math. Soc. 131 (2003) 11, 3387-3393. MR1990627 (2004c:16013)
17. I.M. Gelfand, V.A. Ponomarev, Model algebras and representations of graphs, Funkc. Anal. Priloz. 13 (1979), 1-12. MR0545362 (82a:16030)
18. D. Happel, Hochschild cohomology of finite dimensional algebras, in: Seminaire d'Algebre Paul Dubreil et Marie-Paul Malliavin, in: Lecture Notes in Math., Vol. 1404, Springer-Verlag, Berlin/New York, 1989, pp. 108-126. MR1035222 (91b:16012)
19. D. Happel, U. Preiser, C.M. Ringel
20. D. Happel, U. Preiser, C.M. Ringel, Vinberg's characterization of Dynkin diagrams using subadditive functions with application to D Tr-periodic modules, in: Representation Theory II, in: Lecture Notes in Math., Vol. 832, Springer-Verlag, Berlin/New York, 1980, pp. 280-294. MR0607159 (82g:16027)
21. P. Kronheimer, The construction of ALE spaces as hyper-Kahler quotients, Diff. Geom. 29 (1989), 665-683. MR0992334 (90d:53055)
22. G. Lusztig, Quivers, perverse sheaves and quantized enveloping algebras, J.Amer. Math. Soc. 4 (1991), 365-421. MR1088333 (91m:17018)
23. G. Lusztig, Affine quivers and canonical bases, Publ. IHES 76 (1992), 111-163.
24. C. Riedtmann, Algebren, Darstellungskocher und zurack, Comment Math. Helv. 55 (1980), 199-224. MR0576602 (82k:16039)
25. C.M. Ringel, The preprojective algebra of tame quiver: the irreducible components of the module varieties, in: Trends in the Representation Theory of Finite Dimensional Algebras, Contemp. Math., Vol. 229, Amer. Math. Soc., Providence, RI, 1998, pp. 293306. MR1676227 (2000b:16028)
26. C.M. Ringel, The preprojective algebra of a quiver, in: Algebras and Modules II, CMS Conference Proceedings, Vol. 24, Amer. Math. Soc., Providence, RI, 1998, pp. 467-480. MR1648647 (99i:16031)
27. A. Schofield, Wild algebras with periodic Auslander-Reiten translate, manuscript.
28. K. Yamagata, Frobenius algebras, in: Handbook of algebra, Vol. 1, Amsterdam/New York, Elsevier 1996, pp. 841-887. MR1421820 (97k:16022)