Abstract
Let 𝒞 be a Hom-finite triangulated 2-Calabi–Yau category with a cluster-tilting object. Under some constructibility assumptions on 𝒞 which are satisfied, for instance, by cluster categories, by generalized cluster categories and by stable categories of modules over a preprojective algebra of Dynkin type, we prove a multiplication formula for the cluster character associated with any cluster-tilting object. This formula generalizes those obtained by Caldero–Keller for representation finite path algebras and by Xiao–Xu for finite-dimensional path algebras. We prove an analogous formula for the cluster character defined by Fu–Keller in the set-up of Frobenius categories. It is similar to a formula obtained by Geiss–Leclerc–Schröer in the context of preprojective algebras.
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