Modules over cluster-tilted algebras determined by their dimension   vectors
  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. 
Ibrahim Assem and Gr\'egoire Dupont
math.RT math.RA