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Quasitilted algebras admit a preprojective component
Author(s):
Flavio
U.
Coelho;
Dieter
Happel
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1283-1291.
MSC (1991):
Primary 16G10, 16E10
MathSciNet review:
1363416
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Abstract:
Quasitilted algebras are generalizations of tilted algebras. As a main result we show here that the Auslander-Reiten quiver of such an algebra has a preprojective component
References:
- [ARS]
- Auslander, M.; Reiten, I.; Smalø, S., Representation theory of Artin algebras, Cambridge University Press 36 (1995). MR 96c:16015
- [B]
- Bongartz, K., A criterion for finite representation type, Math. Ann. 269 (1984), 1-12. MR 86k:16023
- [CS]
- Coelho, F.U.; Skowronski, A., On the Auslander-Reiten quiver of a quasitilted algebra, Fundamenta Mathematica 149 (1996), 67-82.
- [DP]
- Dräxler, P.; de la Peña, J.A., On the existence of postprojective components in the Auslander-Reiten quiver of an algebra, preprint.
- [HR]
- Happel, D.; Ringel, C.M., Directing projective modules, Archiv Math. 60 (1993), 247-243. MR 94b:16016
- [HRS1]
- Happel, D.; Reiten, I.; Smalø, S., Short cycles and sincere modules, CMS Conference Proceedings 14 (1993), 233-236. CMP 94:09
- [HRS2]
- Happel, D.; Reiten, I.; Smalø, S., Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996), no. 575. CMP 96:08
- [R]
- Ringel, C.M., Tame algebras and integral quadratic forms, Springer Lecture Notes 1099 (1984). MR 87f:16027
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- Skowronski, A., Tame quasitilted algebras, preprint.
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- Strauss, H, The perpendicular category of a partial tilting module, J. Algebra 144 (1991), 43-66. MR 92m:16013
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Additional Information:
Flavio
U.
Coelho
Affiliation:
Instituto de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo, 05389-970, Brasil
Email:
fucoelho@ime.usp.br
Dieter
Happel
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, Postfach 964, 09107 Chemnitz, Germany
Email:
dieter.happel@mathematik.tu-chemnitz.de
DOI:
10.1090/S0002-9939-97-03697-6
PII:
S 0002-9939(97)03697-6
Keywords:
Preprojective components,
quasitilted algebras
Received by editor(s):
March 31, 1995
Received by editor(s) in revised form:
November 10, 1995
Additional Notes:
This work was done when the first named author was visiting the Chemnitz University under the financial support of FAPESP and CNPq, Brazil. He would like to thank the second author for the kind hospitalitly during his stay. The authors also would like to thank J. A. de la Peña for pointing out some inaccuracies in an earlier version.
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
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