Gentle algebras arising from surface triangulations
Representation Theory
2009-07-01 v2
Abstract
In this paper, we associate an algebra A(T) to a triangulation T of a surface S with a set of boundary marking points. This algebra A(T) is gentle and Gorenstein of dimension one. We also prove that A(T) is cluster-tilted if and only if it is cluster-tilted of type A or A tilde, or if and only if the surface S is a disc or an annulus. Moreover all cluster-tilted algebras of type A or A tilde are obtained in this way.
Cite
@article{arxiv.0903.3347,
title = {Gentle algebras arising from surface triangulations},
author = {Ibrahim Assem and Thomas Brüstle and Gabrielle Charbonneau-Jodoin and Pierre-Guy Plamondon},
journal= {arXiv preprint arXiv:0903.3347},
year = {2009}
}
Comments
37 pages, with more examples and details than the first version