Group actions on relative cluster categories and Higgs categories
Abstract
Abstract Let G be a finite group acting on an ice quiver with potential ( Q , F , W ) $(Q, F, W)$ left parenthesis upper Q comma upper F comma upper W right parenthesis . 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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Publication details
- Journal / source
- Nagoya Mathematical Journal
- Publisher
- Cambridge University Press (CUP)
- Volume
- 261
- Publication date
- 1 January 2026
- Language
- EN