Caldero-Keller approach to the denominators of cluster variables

Details Caldero-Keller approach to the denominators of cluster variables Caldero-Keller approach to the denominators of cluster variables

2007-11-29

arxiv.org/abs/0711.4661v2

Mathematics

Representation Theory

10 pages. Minor modifications : mainly layout and typos

Scientific paper

Buan, Marsh and Reiten proved that if a cluster-tilting object $T$ in a cluster category $\mathcal C$ associated to an acyclic quiver $Q$ satisfies certain conditions with respect to the exchange pairs in $\mathcal C$, then the denominator in its reduced form of every cluster variable in the cluster algebra associated to $Q$ has exponents given by the dimension vector of the corresponding module over the endomorphism algebra of $T$. In this paper, we give an alternative proof of this result using the Caldero-Keller approach to acyclic cluster algebras and the work of Palu on cluster characters.

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