论文标题
自注射2-卡拉比 - YAU倾斜代数的派生等效性
Derived equivalences of self-injective 2-Calabi--Yau tilted algebras
论文作者
论文摘要
考虑使用投影生成器的$ k $ -linear frobenius类别$ \ mathscr {e} $，以便相应的稳定类别$ \ mathscr {c} $ is 2-calabi - yau，yyau，hom-finite，hom-finite ting split idempotents。令$ l，m \ in \ mathscr {c} $为具有自注射的内态代数的最大刚性对象。我们将证明他们的内态代数$ \ mathscr {c}（l，l，l）$和$ \ mathscr {c}（m，m）$是派生的。此外，我们将描述两面倾斜复合物，该复合物引起了这种衍生的等效性。
Consider a $k$-linear Frobenius category $\mathscr{E}$ with a projective generator such that the corresponding stable category $\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in\mathscr{C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras $\mathscr{C}(l,l)$ and $\mathscr{C}(m,m)$ are derived equivalent. Furthermore we will give a description of the two-sided tilting complex which induces this derived equivalence.
