Classifying tame blocks and related algebras up to stable equivalences of Morita type

We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of the class of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain as byproduct the validity of the Auslander-Reiten conjecture for these classes of algebras

Batalin-Vilkovisky structure over the Hochschild cohomology ring of a group algebra

We realize explicitly the well-known additive decomposition of the Hochschild cohomology ring of a group algebra in the elements level. As a result, we describe the cup product, the Batalin-Vilkovisky operator and the Lie bracket in the Hochschild cohomology ring of a group algebra.Comment: This paper uses a Maple program which is avaible at http://math.bnu.edu.cn/~liuym

Two questions on stable equivalences of Morita type

It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.Comment: 9 page