On Stable Equivalences of Morita Type for Finite Dimensional Algebras
نویسنده
چکیده
In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module to a simple B-module, then N⊗A− 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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