English

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.

Keywords

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

R2 v1 2026-06-21T20:25:06.852Z