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Linear independence of cluster monomials for skew-symmetric cluster algebras. (English) Zbl 1288.18011
The authors show that cluster monomials are linearly independent in any cluster algebra associated with a skew-symmetric matrix. As a consequence, they obtain that for a skew-symmetric cluster algebra the exchange graph and the cluster complex only depend on its defining matrix. These results confirm conjectures of Fomin and Zelevinsky for this class of cluster algebras.

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
13F60 Cluster algebras
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