Equivalences Of Morita Type Research Articles

On Stable Equivalence of Tensor Products of Algebras

The paper investigates the following problem. Let bimodules N, M yield a stable equivalence of Morita type between self-injective K-algebras A and E. Further, let bimodules S, T yield a stable equivalence of Morita type between self-injective K-algebras B and F. Then we want to know whether the functor M ⊗ A − ⊗ B S: mod(A ⊗ K B op ) → mod(E ⊗ K F op ) induces a stable equivalence between A ⊗ K B op and E ⊗ K F op . There is given a reduction of this problem to some smaller subcategories for self-injective algebras. Moreover, new invariants of stable equivalences of Morita type are constructed in a general case of arbitrary finite-dimensional algebras over a field.

Orbit algebras that are invariant under stable equivalences of Morita type

AbstractIn this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.

Module-relative-Hochschild (co)homology under stable equivalences of Morita type

Based on the theory of relative right derived functors, module-relative-Hochschild cohomology was introduced by Ardizzoni, Brzezin′ski and Menini when they studied the formal smoothness. In this paper, we introduce the module-relative-Hochschild homology using relative left derived functors, discuss the relations of Hochschild (co)homology, relative Hochschild (co)homology and module-relative-Hochschild (co)homology under stable equivalences of Morita type, and prove that module-relative-Hochschild homology and cohomology are invariants under stable equivalences of Morita type. As a consequence, we get a method of constructing formally smooth bimodules and separable bimodules, and give a new proof to the known fact that the stable equivalence of Morita type preservers the ordinary Hochschild (co)homology.

Stable equivalences of Morita type and stable Hochschild cohomology rings

We prove that a stable equivalence of Morita type between finite dimensional algebras preserves the stable Hochschild cohomology rings, that is, Hochschild cohomology rings modulo the projective center, thus generalizing the results of Pogorzaly and Xi.

Summands of Stable Equivalences of Morita Type

A stable equivalence of Morita type between two finite dimensional algebras with no separable summand will be shown to restrict to stable equivalences of Morita type between their summands. We will apply this to prove that stable equivalence of Morita type preserves self-injectivity of algebras and the property of being symmetric.

Derived equivalences of selfinjective algebras preserve singularities

We prove that the derived equivalences (more generally the stable equivalences of Morita type) of finite dimensional selfinjective algebras over algebraically closed fields preserve the types of singularities in the orbit closures of module varieties. As an application, we obtain that the orbit closures in the module varieties of the Brauer tree algebras are normal and Cohen-Macaulay.

Representation type and stable equivalence of Morita type for finite dimensional algebras

Representation type and stable equivalence of Morita type for finite dimensional algebras

Equivalences induced by graded bimodules

Let k be a commutative ringG a finite groupR and S fully G-graded k-algebras. In this paper we investigate Morita equivalences, derived equivalences and stable equivalences of Morita type between R and S, which are induced by G-graded R, 5-bimodules or complexes of G-graded bimodules. Such equivalences occur naturally in the case of group algebras in certain reduction steps for Broue's conjecture, and we show how they can be lifted from equivalences between R 1 and S 1.

Stable equivalences of Morita type for self-injective algebras and p-groups

Stable equivalences of Morita type for self-injective algebras and p-groups