Modules Over Cluster-Tilted Algebras Determined by Their Dimension Vectors |
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Authors: | Ibrahim Assem |
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Institution: | Université de Sherbrooke , Sherbrooke , Quebec , Canada |
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Abstract: | We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed algebras, rigid modules lifting to rigid objects in the corresponding cluster category are uniquely determined by their dimension vectors. Finally, we apply our results to a conjecture of Fomin and Zelevinsky on denominators of cluster variables. |
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Keywords: | Cluster-tilted algebras Cluster-concealed algebras Cluster algebras Cluster variables Denominators Dimension vectors |
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