Crossed-products of Calabi-Yau algebras by finite groups

Patrick Le Meur (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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.

Mots clés: Calabi-Yau algebras; skew group algebras; quivers with potentials; Ginzburg algebras; cluster categories; higher Auslander-Reiten theory

Domaines: Anneaux et algèbres [math.RA]

Patrick Le Meur. Crossed-products of Calabi-Yau algebras by finite groups. Journal of Pure and Applied Algebra, 2020, 224 (10), pp.106394. ⟨10.1016/j.jpaa.2020.106394⟩. ⟨hal-00488814v3⟩