paper

The cluster multiplication theorem for acyclic quantum cluster algebras

arXiv:2108.03558

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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