Clusters and seeds in acyclic cluster algebras

Abstract

We show that for cluster algebras associated with finite quivers without oriented cycles (with no coefficients), a seed is determined by its cluster, as conjectured by Fomin and Zelevinsky.We also obtain an interpretation of the monomial in the denominator of a non-polynomial cluster variable in terms of the composition factors of an indecomposable exceptional module over an associated hereditary algebra.

12 pages, version3: added an appendix coauthored in addition by P. Caldero and B. Keller

References in corpus (1)

• Quivers with relations and cluster tilted algebras

Cited by in corpus (2)

• Some Remarks Concerning Tilting Modules and Tilted Algebras. Origin. Relevance. Future. (An appendix to the Handbook of Tilting Theory)
• From triangulated categories to cluster algebras