On singular equivalences of Morita type with level and Gorenstein algebras

Abstract

Rickard proved that for certain self-injective algebras, a stable equivalence induced from an exact functor is a stable equivalence of Morita type, in the sense of Broué. In this paper we study singular equivalences of finite dimensional algebras induced from tensor product functors. We prove that for certain Gorenstein algebras, a singular equivalence induced from tensoring with a suitable complex of bimodules, induces a singular equivalence of Morita type with level, in the sense of Wang. This recovers Rickard's theorem in the self-injective case.

Final version. The proof of the main Corollary is now fixed as well as some typos in 3.6, 3.7. To appear in the Bulletin of the London Mathematical Society