论文标题
双模模诱导的奇异等效量和二次单元代数
Singular equivalences induced by bimodules and quadratic monomial algebras
论文作者
论文摘要
当双模模量产生奇异等效性时，我们研究了问题。事实证明，当相同双模模给出的HOM函子诱导Injective模块的无循环复合物之间的同型类别之间的三角形等效性时，这个问题等效于一个问题。我们给出条件，何时在一对双模模中出现双模模，该双模模定义了与水平的奇异等效性。我们构建一个明确的双模模，该双模模产生了二次单数代数与其相关代数与自由基平方零之间的奇异等效性。在包括戈伦斯坦病例在内的某些条件下，双模模的确出现在一对定义与水平的奇异等效性的双模型中。
We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between the homotopy categories of acyclic complexes of injective modules. We give conditions on when a bimodule appears in a pair of bimodules, that defines a singular equivalence with level. We construct an explicit bimodule, which yields a singular equivalence between a quadratic monomial algebra and its associated algebra with radical square zero. Under certain conditions which include the Gorenstein cases, the bimodule does appear in a pair of bimodules defining a singular equivalence with level.
