论文标题
关于Morita类型的奇异等价，级别和Gorenstein代数
On singular equivalences of Morita type with level and Gorenstein algebras
论文作者
论文摘要
里卡德（Rickard）证明，对于某些自我注射代数，从确切的函子引起的稳定等效性是莫里塔（Morita）类型的稳定等效性，就布鲁埃（Broué）而言。在本文中，我们研究了张量产物函子引起的有限尺寸代数的奇异等效性。我们证明，对于某些Gorenstein代数，这是一种由合适的双模型复合物张紧引起的奇异等效性，从王的意义上讲，莫里塔类型与水平的奇异等效性。在自注明的情况下，这恢复了里卡德的定理。
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.
