A Geometric Model for the Module Category of a Gentle Algebra

By Karin Baur, Raquel Coelho Guardado Simões. International mathematics research notices, 2018

88 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fd3a6ae82451912aa9c55fc0e67b1497e734e4c6

Citations in the corpus

• A complete derived invariant for gentle algebras via winding numbers and Arf invariants (2019, unknown): “It turns out that any gentle algebra can be obtained from a dissection of a surface; this has led to geometric models for their module categories [BCS18] (building on [CSP16]) and τ -tilting theory [PPP18] (see also [BDM17, PPP17]).”