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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

Downloaded from
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