Abstract
Abstract Let $Q$ be a finite acyclic valued quiver. We give the cluster multiplication formulas in the quantum cluster algebra of $Q$ with arbitrary coefficients, by applying certain quotients of derived Hall subalgebras of $Q$. 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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