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The Yoneda algebras of symmetric special biserial algebras are finitely generated
Author(s):
M.
A.
Antipov;
A.
I.
Generalov
Translated by:
M. A. Antipov
Original publication:
Algebra i Analiz,
tom 17
(2005),
vypusk 3.
Journal:
St. Petersburg Math. J.
17
(2006),
377-392.
MSC (2000):
Primary 20C05
Posted:
March 9, 2006
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Additional information
Abstract:
By using the Benson-Carlson diagrammatic method, a detailed combinatorial description is given for the syzygies of simple modules over special biserial algebras. With the help of this description, it is proved that the Yoneda algebras of the algebras mentioned above are finitely generated.
References:
-
- 1.
- P. Gabriel and Ch. Riedtmann, Group representations without groups, Comment. Math. Helv. 54 (1979), 240-287. MR 0535058 (80k:16040)
- 2.
- Ch. Riedtmann, Representation-finite self-injective algebras of class
 , Representation Theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., vol. 832, Springer, Berlin, 1980, pp. 449-520. MR 0607169 (82k:16040) - 3.
- E. S. Golod, The cohomology ring of a finite
 -group, Dokl. Akad. Nauk SSSR 125 (1959), no. 4, 703-706. (Russian) MR 0104720 (21:3473) - 4.
- B. B. Venkov, Cohomology algebras for some classifying spaces, Dokl. Akad. Nauk SSSR 127 (1959), no. 5, 943-944. (Russian) MR 0108788 (21:7500)
- 5.
- L. Evens, The cohomology ring of a finite group, Trans. Amer. Math. Soc. 101 (1961), 224-239. MR 0137742 (25:1191)
- 6.
- E. M. Friedlander and A. Suslin, Cohomology of finite group schemes over a field, Invent. Math. 127 (1997), no. 2, 209-270. MR 1427618 (98h:14055a)
- 7.
- B. Wald and J. Waschbüsch, Tame biserial algebras, J. Algebra 95 (1985), 480-500. MR 0801283 (87a:16056)
- 8.
- K. Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Math., vol. 1428, Springer-Verlag, Berlin, 1990, 312 pp. MR 1064107 (91c:20016)
- 9.
- D. J. Benson and J. F. Carlson, Diagrammatic methods for modular representations and cohomology, Comm. Algebra 15 (1987), no. 1-2, 53-121. MR 0876974 (87m:20032)
- 10.
- A. I. Generalov, Cohomology of algebras of dihedral type. I, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 265 (1999), 139-162; English transl., J. Math. Sci. (New York) 112 (2002), no. 3, 4318-4331. MR 1757820 (2001b:20090)
- 11.
- O. I. Balashov and A. I. Generalov, The Yoneda algebras for some class of dihedral algebras, Vestnik S.-Peterburg. Univ. Ser. 1 1999, vyp. 3, 3-10; English transl., Vestnik St. Petersburg Univ. Math. 32 (1999), no. 3, 1-8 (2000). MR 1794988 (2001m:16020)
- 12.
- M. C. R. Butler and C. M. Ringel, Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra 15 (1987), no. 1-2, 145-179. MR 0876976 (88a:16055)
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Additional Information:
M.
A.
Antipov
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Avenue 28, Staryi Peterhof, St. Petersburg 198904, Russia
A.
I.
Generalov
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Avenue 28, Staryi Peterhof, St. Petersburg 198904, Russia
DOI:
10.1090/S1061-0022-06-00909-5
PII:
S 1061-0022(06)00909-5
Keywords:
Yoneda algebra,
special biserial algebras
Received by editor(s):
1/SEP/2004
Posted:
March 9, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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