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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… Click to show full abstract
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.
Journal Title: Journal of Pure and Applied Algebra
Year Published: 2020
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