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## Cluster characters II: A multiplication formula

### Abstract

v3: Updated references. Section on Fu--Keller's cluster character. v4: Some expository changes as suggested by the referee. To appear in Proceedings LMS.Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi--Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster categories and by stable categories of modules over a preprojective algebra, 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. It is analogous to a formula obtained by Geiss--Leclerc--Schröer in the context of preprojective algebras

Topics: 2-Calabi--Yau triangulated categories, cluster characters, cluster algebras, 18E30 ; 16G20, [ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]
Publisher: HAL CCSD
Year: 2011
OAI identifier: oai:HAL:hal-00369263v4
Provided by: Hal-Diderot

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