Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 097, 60 pages      arXiv:2110.12429      https://doi.org/10.3842/SIGMA.2023.097

The Multiplication Formulas of Weighted Quantum Cluster Functions

Zhimin Chen a, Jie Xiao b and Fan Xu c
a)  Department of Mathematics, Tsinghua University, Beijing 100084, P. R. China
b)  School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China
c)  Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

Received June 02, 2022, in final form November 26, 2023; Published online December 13, 2023

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.

Key words: weighted quantum cluster functions; cluster categories; 2-Calabi-Yau triangulated categories; preprojective algebras.

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