Abstract Let a finite group G act on a differential graded algebra A. This article presents necessary conditions and sufficient conditions for the skew group algebra A ⁎ G to be Calabi-Yau. In particular, when A is the Ginzburg dg algebra of a quiver with an invariant potential, then A ⁎ G is Calabi-Yau and Morita equivalent to a Ginzburg dg algebra. Some applications of these results are derived to compare the generalised cluster categories of A and A ⁎ G when they are defined and to compare the higher Auslander-Reiten theories of A and A ⁎ G when A is a finite dimensional algebra.

中文翻译：

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Calabi-Yau 代数的有限群交叉积

摘要 设有限群G作用于微分分级代数A。本文给出偏态群代数A⁎G为Calabi-Yau的充要条件。特别地，当 A 是具有不变势的 quiver 的 Ginzburg dg 代数时，则 A ⁎ G 是 Calabi-Yau 和 Morita 等价于 Ginzburg dg 代数。推导出这些结果的一些应用，以比较定义时 A 和 A ⁎ G 的广义聚类类别，以及当 A 是有限维代数时比较 A 和 A ⁎ G 的高级 Auslander-Reiten 理论。