Motivic cluster multiplication formulas in 2-Calabi-Yau categories
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911761534287872 |
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| author | Xiao, Jie Xu, Fan Yang, Fang |
| author_facet | Xiao, Jie Xu, Fan Yang, Fang |
| contents | We introduce a notion of motivic cluster characters via virtual Poincaré polynomials, and prove a motivic version of multiplication formulas obtained by Chen-Xiao-Xu for weighted quantum cluster characters associated to a 2-Calabi-Yau triangulated category $\mathcal{C}$ with a cluster tilting object. Furthermore, a refined form of this formula is also given. When $\mathcal{C}$ is the cluster category of an acyclic quiver, our certain refined multiplication formula is a motivic version of the multiplication formula in [International Mathematics Research Notices, rnad172(2023)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04849 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Motivic cluster multiplication formulas in 2-Calabi-Yau categories Xiao, Jie Xu, Fan Yang, Fang Representation Theory 17B37, 16G20, 17B20 We introduce a notion of motivic cluster characters via virtual Poincaré polynomials, and prove a motivic version of multiplication formulas obtained by Chen-Xiao-Xu for weighted quantum cluster characters associated to a 2-Calabi-Yau triangulated category $\mathcal{C}$ with a cluster tilting object. Furthermore, a refined form of this formula is also given. When $\mathcal{C}$ is the cluster category of an acyclic quiver, our certain refined multiplication formula is a motivic version of the multiplication formula in [International Mathematics Research Notices, rnad172(2023)]. |
| title | Motivic cluster multiplication formulas in 2-Calabi-Yau categories |
| topic | Representation Theory 17B37, 16G20, 17B20 |
| url | https://arxiv.org/abs/2310.04849 |