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Clusters and seeds in acyclic cluster algebras

Aslak Bakke Buan·Bethany Marsh·Idun Reiten·Gordana Todorov
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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.

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Aslak Bakke Buan, Bethany Marsh, Idun Reiten, Gordana Todorov. 2007-03-08. Clusters and seeds in acyclic cluster algebras. https://arxiv.org/abs/math/0510359

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