On stable equivalences induced by exact functors
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Abstract:
Let $A$ and $B$ be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence $\alpha$ between $A$ and $B$ such that $\alpha$ is induced by exact functors. We present a nice correspondence between indecomposable modules over $A$ and $B$. As a consequence, we have the following: (1) If $A$ is a self-injective algebra, then so is $B$; (2) If $A$ and $B$ are finite dimensional algebras over an algebraically closed field $k$, and if $A$ is of finite representation type such that the Auslander-Reiten quiver of $A$ has no oriented cycles, then $A$ and $B$ are Morita equivalent.References
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Additional Information
- Yuming Liu
- Affiliation: School of Mathematical Sciences, Beijing Normal University, 100875 Beijing, People’s Republic of China
- MR Author ID: 672042
- Email: liuym2@263.net
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2204270