Cluster algebras from cluster categories

Philippe Caldero (1) , Frédéric Chapoton (1)

1 IGD - Institut Girard Desargues

Cluster categories are triangulated categories which were recently introduced in connection with the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding cluster category. This also provides some explicit formulas for cluster variables.

Mots clés: cluster algebra; triangulated category; quiver representation

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

Philippe Caldero, Frédéric Chapoton. Cluster algebras from cluster categories. 2004. ⟨hal-00003015v1⟩