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arXiv · 2310.04849

Motivic cluster multiplication formulas in 2-Calabi-Yau categories

Jie Xiao·Fan Xu·Fang Yang
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Abstract

We introduce a notion of motivic cluster characters via virtual Poincar\'{e} 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)].

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BibTeXRIS

Jie Xiao, Fan Xu, Fang Yang. 2023-10-07. Motivic cluster multiplication formulas in 2-Calabi-Yau categories. https://arxiv.org/abs/2310.04849

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