|
Generalized Auslander-Reiten conjecture and tilting equivalences
Author(s):
Jiaqun
Wei
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1581-1585.
MSC (2000):
Primary 16E10, 16E30, 16E65
Posted:
December 21, 2009
MathSciNet review:
2587442
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that the generalized Auslander-Reiten conjecture is stable under tilting equivalences.
References:
-
- 1.
- M. Auslander and I. Reiten, On a generalized version of the Nakayama conjecture, Proc. Amer. Math. Soc. 52 (1975), 69-74. MR 0389977 (52:10806)
- 2.
- M. Auslander and I. Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1) (1991), 111-152. MR 1097029 (92e:16009)
- 3.
- Y. Miyashita, Tilting modules of finite projective dimension, Math. Zeit. 193 (1986), 113-146. MR 852914 (87m:16055)
- 4.
- S. Pan and C. Xi, Finiteness of finitistic dimension is invariant under derived equivalences, Journal of Algebra 322 (2009), 21-24. MR 2526372
- 5.
- D. Happel, Reduction techniques for homological conjectures, Tsukuba J. Math. 17 (1) (1993), 115-130. MR 1233117 (94h:16015)
- 6.
- D. Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Soc. Lect. Note Ser., 119, Cambridge Univ. Press, Cambridge, 1988. MR 935124 (89e:16035)
- 7.
- H. Tachikawa, Quasi-Frobenius rings and generalizations, Lect. Notes Math., 351, Springer-Verlag, Berlin-New York, 1973. MR 0349740 (50:2233)
- 8.
- J. Wei, Finitistic dimension and restricted flat dimension, J. Algebra 320 (2008), 116-127. MR 2417981 (2009e:16013)
- 9.
- J. Wei, A note on Auslander bounds, arXiv: 0802.1085v2.
- 10.
- J. Wei and C. Xi, A characterization of the tilting pair, J. Algebra 317 (2007), 376-391. MR 2360155 (2009b:16034)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
16E10, 16E30, 16E65
Retrieve articles in all Journals with
MSC (2000):
16E10, 16E30, 16E65
Additional Information:
Jiaqun
Wei
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210046, People's Republic of China
Address at time of publication:
Mathematisches Institut, Universität zu Koeln, Weyertal 86-90, D-50931 Koeln, Germany
Email:
weijiaqun@njnu.edu.cn
DOI:
10.1090/S0002-9939-09-10153-3
PII:
S 0002-9939(09)10153-3
Keywords:
Auslander-Reiten conjecture tilting equivalence
Received by editor(s):
March 29, 2009,
Received by editor(s) in revised form:
June 20, 2009, and July 23, 2009
Posted:
December 21, 2009
Additional Notes:
The author is supported by the National Science Foundation of China (Grants No. 10601024 and 10971099) and partially by the Jiangsu Natural Science Foundation (Grant No. BK2007220)
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2009,
American Mathematical Society
|