网格代数的分解：周期性和Calabi-Yau维数
Resolutions of mesh algebras: periodicity and Calabi-Yau dimensions
摘要：
一个三角范畴称为d维卡-丘范畴，如果它的悬置的d次方是一个塞尔函子。我们确定了有限表示型自内射代数A的稳定范畴是Calabi-Yau的，并计算了它们的Calabi-Yau维数。我们通过研究A的稳定Auslander代数在其包络代数上的最小投射分解来实现这一点，并利用覆盖理论将其约化为Dynkin图的（广义）预投射代数.我们还描述了如何解决这个问题，实现稳定的类别问题的轨道类别的有界导出范畴的遗传代数。
英文摘要：
A triangulated category is said to be Calabi-Yau of dimension d if the dth power of its suspension is a Serre functor. We determine which stable categories of self-injective algebras A of finite representation type are Calabi-Yau and compute their Calabi-Yau dimensions. We achieve this by studying the minimal projective resolution of the stable Auslander algebra of A over its enveloping algebra, and use covering theory to reduce to (generalized) preprojective algebras of Dynkin graphs. We also describe how this problem can be approached by realizing the stable categories in question as orbit categories of the bounded derived categories of hereditary algebras.
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