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Pré-Publication, Document De Travail Année : 2011

Cluster characters II: A multiplication formula

Yann Palu

Résumé

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.
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Dates et versions

hal-00369263 , version 1 (18-03-2009)
hal-00369263 , version 2 (18-05-2009)
hal-00369263 , version 3 (11-06-2010)
hal-00369263 , version 4 (08-06-2011)

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Yann Palu. Cluster characters II: A multiplication formula. 2011. ⟨hal-00369263v4⟩
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