Rigid and Schurian modules over cluster-tilted algebras of tame type
Representation Theory
2020-12-21 v2 Rings and Algebras
Abstract
We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra A, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid A-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid A-modules in this case.
Keywords
Cite
@article{arxiv.1412.6405,
title = {Rigid and Schurian modules over cluster-tilted algebras of tame type},
author = {Bethany Marsh and Idun Reiten},
journal= {arXiv preprint arXiv:1412.6405},
year = {2020}
}
Comments
39 pages, no separate figures