A geometric model for the module category of a gentle algebra

Baur, Karin and Coelho Guardado Simoes, Raquel (2021) A geometric model for the module category of a gentle algebra. International Mathematics Research Notices, 2021 (15). pp. 11357-11392. ISSN 1073-7928

Abstract

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian algebras of triangulations of surfaces and the notion of surface algebras. We use this description to give a geometric model of the module category of any gentle algebra.