On stable equivalences induced by exact functors

Author:
Yuming Liu

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1605-1613

MSC (2000):
Primary 16G10; Secondary 16G70

DOI:
https://doi.org/10.1090/S0002-9939-05-08157-8

Published electronically:
December 5, 2005

MathSciNet review:
2204270

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence between and such that is induced by exact functors. We present a nice correspondence between indecomposable modules over and . As a consequence, we have the following: (1) If is a self-injective algebra, then so is ; (2) If and are finite dimensional algebras over an algebraically closed field , and if is of finite representation type such that the Auslander-Reiten quiver of has no oriented cycles, then and are Morita equivalent.

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Additional Information

**Yuming Liu**

Affiliation:
School of Mathematical Sciences, Beijing Normal University, 100875 Beijing, People’s Republic of China

Email:
liuym2@263.net

DOI:
https://doi.org/10.1090/S0002-9939-05-08157-8

Keywords:
Stable equivalence induced by exact functors,
simple module,
indecomposable module

Received by editor(s):
September 28, 2004

Received by editor(s) in revised form:
January 11, 2005

Published electronically:
December 5, 2005

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.