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Crossed-products of Calabi-Yau algebras by finite groups (1006.1082v3)
Published 6 Jun 2010 in math.RA
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.