Caldero-Keller approach to the denominators of cluster variables

2007/11/29 by Grégoire Dupont, Dupont, G.
Computer Science · #16G20 #16G70 #16S99 #Advanced Clustering Algorithms Research #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0711.4661

openalex publication_date 2007/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• On cluster algebras with coefficients and 2-Calabi-Yau categories

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