Zhimin Chen, Jie Xiao, Fan Xu, “The Multiplication Formulas of Weighted Quantum Cluster Functions”, SIGMA, 2023, Volume 19,097, 60 pp.

The Multiplication Formulas of Weighted Quantum Cluster Functions

Zhimin Chen^a, Jie Xiao^b, Fan Xu^a

^a Tsinghua University, Beijing 100084, P. R. China
^b School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

Abstract: By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with Ext-symmetry and 2-Calabi–Yau triangulated categories with cluster-tilting objects.

Keywords: weighted quantum cluster functions, cluster categories, 2-Calabi–Yau triangulated categories, preprojective algebras.

MSC: 17B37, 16G20, 17B20

Received: June 2, 2022; in final form November 26, 2023; Published online December 13, 2023

Language: English

DOI: 10.3842/SIGMA.2023.097