c-vectors and dimension vectors for cluster-finite quivers (Q2865920)
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scientific article; zbMATH DE number 6237639
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | c-vectors and dimension vectors for cluster-finite quivers |
scientific article; zbMATH DE number 6237639 |
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c-vectors and dimension vectors for cluster-finite quivers (English)
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11 December 2013
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cluster algebra
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dimension vector
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mutation
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Dynkin quiver
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Jacobian algebra
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The main result of this note is the observation that a positive \(\mathbf{c}\)-vector associated with a quiver equipped with a non-degenerate potential equals the dimension vector of a certain module for the corresponding Jacobian algebra. As a consequence, it follows that for quivers which are mutation equivalent to a Dynkin quiver the set of positive \(\mathbf{c}\)-vectors equals the set of dimension vectors for indecomposable modules over the corresponding Jacobian algebra. Several examples are provided.
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