Cluster tilting modules for mesh algebras
Representation Theory
2020-07-03 v3
Abstract
We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.
Cite
@article{arxiv.1904.01369,
title = {Cluster tilting modules for mesh algebras},
author = {Karin Erdmann and Sira Gratz and Lisa Lamberti},
journal= {arXiv preprint arXiv:1904.01369},
year = {2020}
}
Comments
comments appreciated; the third version includes a discussion on the combinatorics of the mutations