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arXiv:1203.1307 [math.RT]AbstractReferencesReviewsResources

Linear independence of cluster monomials for skew-symmetric cluster algebras

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

Published 2012-03-06, updated 2013-03-04Version 4

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.

Comments: 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
Categories: math.RT, math.RA
Subjects: 13F60, 18E30
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