论文标题
塞雷函子和分级类别
Serre functors and graded categories
论文作者
论文摘要
我们研究了富含关键单体类别的类别的serre结构，并将其应用于两种分级K线性类别的serre结构：具有分级HOM空间的小组动作和类别的类别。我们检查了通过将轨道类别和偏斜组类别保留的塞雷结构是否可以保存，并描述与渐变的Frobenius代数的关系。使用正式版本的Auslander-Reiten翻译，我们表明D-pressentation有限代数的派生类别在calabi-yau上且仅当其前注射式代数具有有限顺序的Nakayama Automormormormism级。这连接了文献中的各种结果，并提供了分数Calabi-yau代数的新示例。
We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories with group actions and categories with graded hom spaces. We check that Serre structures are preserved by taking orbit categories and skew group categories, and describe the relationship with graded Frobenius algebras. Using a formal version of Auslander-Reiten translations, we show that the derived category of a d-representation finite algebra is fractionally Calabi-Yau if and only if its preprojective algebra has a graded Nakayama automorphism of finite order. This connects various results in the literature and gives new examples of fractional Calabi-Yau algebras.
