On stable equivalences of Morita type for finite dimensional algebras

Author:
Yuming Liu

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2657-2662

MSC (2000):
Primary 16D20; Secondary 16G20

Published electronically:
February 6, 2003

MathSciNet review:
1974320

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Abstract: In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field and modules over an algebra are finitely generated left unitary modules. Let and be two algebras (where is a splitting field for and ) with no semisimple summands. If two bimodules and induce a stable equivalence of Morita type between and , and if maps any simple -module to a simple -module, then is a Morita equivalence. This conclusion generalizes Linckelmann's result for selfinjective algebras. Our proof here is based on the construction of almost split sequences.

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Additional Information

**Yuming Liu**

Affiliation:
Department of Mathematics, Beijing Normal University, 100875 Beijing, People’s Republic of China

Email:
liuym2@263.net

DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06831-X

Received by editor(s):
January 11, 2002

Received by editor(s) in revised form:
April 3, 2002

Published electronically:
February 6, 2003

Communicated by:
Martin Lorenz

Article copyright:
© Copyright 2003
American Mathematical Society