Gentle algebras arising from surface triangulations

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.

37 pages, with more examples and details than the first version

Cited by in corpus (9)

• Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions
• Quivers with potentials associated to triangulated surfaces, Part II: Arc representations
• Coloured quivers for rigid objects and partial triangulations: The unpunctured case
• On Jacobian algebras from closed surfaces
• Positivity for cluster algebras from surfaces
• Categorified canonical bases and framed BPS states
• Generic Modules for string algebras
• Moduli spaces of representations of special biserial algebras
• Cohen-Macaulay Auslander algebras of gentle algebras