17 citations · 64 across the 43 of their papers we have counts for
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The multiplication theorem and bases in finite and affine quantum cluster algebras
Ming Ding, Fan Xu
We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \cite{fanqin}…
Bases of the quantum cluster algebra of the Kronecker quiver
Ming Ding, Fan Xu
We construct bar-invariant bases of the quantum cluster algebra of the Kronecker quiver which are quantum analogues of the canonical basis, semicanonical…
Notes on the cluster multiplication formulas for 2-Calabi-Yau categories
Ming Ding, Fan Xu
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 o…
Hall algebras for odd periodic triangulated categories
Fan Xu, Xueqing Chen
We define the Hall algebra associated to any triangulated category under some finiteness conditions with the -periodic translation functor for odd This generalizes th…
The cluster character for cyclic quivers
Ming Ding, Fan Xu
We define an analogue of the Caldero-Chapoton map (\cite{CC}) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a c…