Group actions on relative cluster categories and Higgs categories

Abstract

Let G be a finite group acting on an ice quiver with potential

. We construct the corresponding G -equivariant relative cluster category and G -equivariant Higgs category, extending the work of Demonet. Using the orbit mutations on the set of G -stable cluster-tilting objects of the Higgs category and an appropriate cluster character, we can link these data to a skew-symmetrizable cluster algebra with coefficients. As a specific example, this provides an additive categorification for cluster algebras with principal coefficients in the non-simply laced case.