Junyang Liu (Paris IMJ), Relative Calabi-Yau structures and ice quivers with potential.

Abstract:

Van den Bergh showed that complete Calabi-Yau algebras are weakly equivalent to deformed dg preprojective algebras. For example, in dimension 3, they are given by quivers with potential. We generalize his theorem to the relative case: under suitable assumptions, relative Calabi-Yau morphisms between complete dg algebras are weakly equivalent to Ginzburg morphisms as introduced by Yeung. For example, in dimension 3, they are given by ice quivers with potential.