Group actions on relative cluster categories and Higgs categories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917475584573440 |
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| author | Wu, Yilin |
| author_facet | Wu, Yilin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group actions on relative cluster categories and Higgs categories Wu, Yilin Representation Theory Rings and Algebras 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. |
| title | Group actions on relative cluster categories and Higgs categories |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2502.10670 |