Linear independence of cluster monomials for skew-symmetric cluster algebras

2012/03/06 by Giovanni Cerulli Irelli, Bernhard Keller, Irelli, Giovanni Cerulli +6 · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RA #math.RT #msc:13F60 #msc:18E30

paper · pdf · doi:10.48550/arxiv.1203.1307

14 pages. v2: Bibliography expanded. v3: Added results 3.7, 3.8, 4.7, 4.8 and 5.6. v4: Added reference and minor changes

arxiv created 2013/03/04 · arxiv updated 2013/03/05

Abstract

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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