Gentle algebras arising from surface triangulations

Abstract

We associate an algebra [math] to a triangulation [math] of a surface [math] with a set of boundary marking points. This algebra [math] is gentle and Gorenstein of dimension one. We also prove that [math] is cluster-tilted if and only if it is cluster-tilted of type [math] or [math] , or if and only if the surface [math] is a disc or an annulus. Moreover all cluster-tilted algebras of type [math] or [math] are obtained in this way.