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.

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关于 Morita 型与水平和 Gorenstein 代数的奇异等价

Rickard 证明了对于某些自注入代数，从精确函子导出的稳定等价是 Morita 类型的稳定等价，在 Broué 的意义上。在本文中，我们研究了从张量积函子导出的有限维代数的奇异等价。我们证明，对于某些 Gorenstein 代数，从使用合适的双模复形张量导出的奇异等价会在 Wang 的意义上诱导 Morita 类型与水平的奇异等价。这恢复了自注入情况下的 Rickard 定理。