Modules over cluster-tilted algebras determined by their dimension vectors
Representation Theory
2012-02-28 v1 Rings and Algebras
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.
Cite
@article{arxiv.1202.5698,
title = {Modules over cluster-tilted algebras determined by their dimension vectors},
author = {Ibrahim Assem and Grégoire Dupont},
journal= {arXiv preprint arXiv:1202.5698},
year = {2012}
}
Comments
9 pages