The cluster multiplication theorem for acyclic quantum cluster algebras
Xueqing Chen, Ming Ding, Haicheng Zhang
TL;DR
This paper establishes quantum cluster multiplication formulas for acyclic valued quivers, extending classical results to the quantum setting using derived Hall algebra techniques.
Contribution
It introduces quantum cluster multiplication formulas for acyclic quivers with arbitrary coefficients, generalizing classical theorems to the quantum context.
Findings
Formulas generalize classical cluster multiplication theorems to quantum algebras.
Uses quotients of derived Hall subalgebras to derive multiplication rules.
Applicable to acyclic valued quivers with arbitrary coefficients.
Abstract
Let be a finite acyclic valued quiver. We give the cluster multiplication formulas in the quantum cluster algebra of with arbitrary coefficients, by applying certain quotients of derived Hall subalgebras of . These formulas can be viewed as the quantum version of the cluster multiplication theorem in the classical cluster algebra proved by Caldero-Keller for finite type, Hubery for affine type and Xiao-Xu for acyclic quivers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons