Modules over cluster-tilted algebras determined by their dimension vectors (1202.5698v1)

Published 25 Feb 2012 in math.RT and math.RA

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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