Linear independence of cluster monomials for skew-symmetric cluster algebras (Q2860720)
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scientific article; zbMATH DE number 6231007
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear independence of cluster monomials for skew-symmetric cluster algebras |
scientific article; zbMATH DE number 6231007 |
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Linear independence of cluster monomials for skew-symmetric cluster algebras (English)
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20 November 2013
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cluster algebra
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cluster category
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cluster monomials
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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.
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