The Multiplication Formulas of Weighted Quantum Cluster Functions
Zhimin Chen, Jie Xiao, Fan Xu
TL;DR
This paper introduces weighted quantum cluster functions and establishes their multiplication formulas within specific algebraic categories, advancing the understanding of quantum cluster algebra structures.
Contribution
It develops the concept of weighted quantum cluster functions and proves their multiplication formulas in Ext-symmetric and 2-Calabi-Yau categories.
Findings
Established multiplication formulas for weighted quantum cluster functions
Extended the framework to abelian and 2-Calabi-Yau categories
Provided new tools for quantum cluster algebra research
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra