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arXiv · 2001.05749

On singular equivalences of Morita type with level and Gorenstein algebras

Georgios Dalezios
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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 Brou\'{e}. 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.

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Georgios Dalezios. 2020-01-16. On singular equivalences of Morita type with level and Gorenstein algebras. https://arxiv.org/abs/2001.05749

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