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arXiv · 2502.10670

Group actions on relative cluster categories and Higgs categories

Yilin Wu
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Abstract

Let $G$ be a finite group acting on an ice quiver with potential $(Q, F, W)$. 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 an explicit 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.

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Yilin Wu. 2025-02-15. Group actions on relative cluster categories and Higgs categories. https://doi.org/10.1017/nmj.2026.10112

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