|
The strong no loop conjecture for special biserial algebras
Author(s):
Shiping
Liu;
Jean-Philippe
Morin
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3513-3523.
MSC (2000):
Primary 16E05
Posted:
June 2, 2004
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We establish the strong no loop conjecture for some special cases, in particular, for special biserial algebras.
References:
-
- 1.
- M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics 36 (Cambridge University Press, Cambridge, 1995). MR 96c:16015
- 2.
- W. D. Burgess and M. Saoín, Homological aspects of semigroup gradings on rings and algebras, Canad. J. Math. 51(3) (1999) 488 - 505. MR 2000i:16089
- 3.
- M. C. R. Butler and C. M. Ringel, Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra 15 (1987) 145 - 179. MR 88a:16055
- 4.
- I. M. Gelfand and V. A. Ponomarev, Indecomposable representations of the Lorentz group, Russian Math. Surveys 23 (1968) 1 - 58. MR 37:5325
- 5.
- E. L. Green, Ø. Solberg and D. Zacharia, Minimal projective resolutions, Trans. Amer. Math. Soc. 353 (2001), 2915-2939. MR 2002c:16010
- 6.
- K. Igusa, Notes on the no loop conjecture, J. Pure Appl. Algebra 69(2) (1990) 161 - 176. MR 92b:16013
- 7.
- J. P. Janusz, Indecomposable modules for finite groups, Ann. Math. 89 (1969) 209 - 241. MR 39:5622
- 8.
- H. Lenzing, Nilpotente Elemente in Ringen von Endlicher Globaler Dimension, Math. Z. 108 (1969) 313 - 324.MR 39:1498
- 9.
- A. Skowronski and J. Waschbüsch, Representation-finite biserial algebras, J. Reine Angew Math. 345 (1983) 172 - 181. MR 85e:16051
- 10.
- B. Wald and J. Waschbüsch, Tame biserial algberas, J. Algebra 95 (1985) 480 - 500. MR 87a:16056
- 11.
- D. Zacharia, Special monomial algebras of finite global dimension, NATO Adv. Sci. Inst. 233 (Kluwer, Dordrecht, 1988) 375 - 378. MR 91d:16015
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
16E05
Retrieve articles in all Journals with MSC
(2000):
16E05
Additional Information:
Shiping
Liu
Affiliation:
Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
Email:
shiping.liu@usherbrooke.ca
Jean-Philippe
Morin
Affiliation:
Département de Mathématiques et d'Informatique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
Email:
jphil18@hotmail.com.
DOI:
10.1090/S0002-9939-04-07512-4
PII:
S 0002-9939(04)07512-4
Received by editor(s):
April 22, 2003
Received by editor(s) in revised form:
May 10, 2003 and September 4, 2003
Posted:
June 2, 2004
Dedicated:
Dedicated to Claus M. Ringel on the occasion of his $60$th birthday
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2004,
American Mathematical Society
|
Comments: webmaster@ams.org