Linear independence of cluster monomials for skew-symmetric cluster algebras

Bernhard Keller; Daniel Labardini-Fragoso; Giovanni Cerulli Irelli; Pierre-Guy Plamondon

arxiv: 1203.1307 · v4 · pith:F76NIMQWnew · submitted 2012-03-06 · 🧮 math.RT · math.RA

Linear independence of cluster monomials for skew-symmetric cluster algebras

Giovanni Cerulli Irelli , Bernhard Keller , Daniel Labardini-Fragoso , Pierre-Guy Plamondon This is my paper

classification 🧮 math.RT math.RA

keywords clusteralgebrasindependentmonomialsskew-symmetricalgebrachoicecoefficients

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Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all skew-symmetric cluster algebras.

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Linear independence of cluster monomials for skew-symmetric cluster algebras

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