Skew group algebras of Calabi–Yau algebras

The Calabi–Yau property of skew group algebras is discussed. It is shown that the skew group algebra A#G of a Koszul Calabi–Yau algebra A with a finite subgroup G of automorphisms of A is Calabi–Yau if and only if G is a finite subgroup of the special linear group SL(A), which is defined by means of the homological determinant. Using the A∞-algebra structure on the Yoneda algebra, some results in Bocklandt et al. (2010) [BSW] are generalized, say, every connected graded p-Koszul Calabi–Yau algebra is derived from a superpotential. The superpotential for the skew group algebra A#G is also constructed.