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A new invariant of stable equivalences of Morita type. (English) Zbl 1062.16003

Summary: It was proved in an earlier paper by the author that the Hochschild cohomology algebras of self-injective algebras are invariant under stable equivalences of Morita type. In this note we show that the orbit algebra of a self-injective algebra \(A\) (considered as an \(A\)-\(A\)-bimodule) is also invariant under stable equivalences of Morita type, where the orbit algebra is the algebra of all stable \(A\)-\(A\)-bimodule morphisms from the non-negative Auslander-Reiten translations of \(A\) to \(A\).

MSC:

16D90 Module categories in associative algebras
16D50 Injective modules, self-injective associative rings
16G20 Representations of quivers and partially ordered sets
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
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