Notes on the cluster multiplication formulas for 2-Calabi-Yau categories
Ming Ding, Fan Xu
TL;DR
This paper develops a new variant of cluster multiplication formulas for 2-Calabi-Yau categories, extending Palu's work and applying it to acyclic quivers within cluster categories.
Contribution
It introduces a modified cluster multiplication formula specifically tailored for acyclic quivers in 2-Calabi-Yau categories, building on Palu's generalization.
Findings
Derived a new cluster multiplication formula for acyclic quivers
Extended Palu's formulas to a variant applicable in cluster categories
Provided theoretical foundations for further research in cluster algebra representations
Abstract
Y. Palu has generalized the cluster multiplication formulas to 2-Calabi-Yau categories with cluster tilting objects (\cite{Palu2}). The aim of this note is to construct a variant of Y. Palu's formula and deduce a new version of the cluster multiplication formula (\cite{XiaoXu}) for acyclic quivers in the context of cluster categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra