A geometric model for the module category of a skew-gentle algebra
Representation Theory
2023-04-05 v4 Rings and Algebras
Abstract
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain indecomposable modules, interpret the Auslander-Reiten translation via the tagged rotation, and show intersection-dimension formulas. As an application, we classify support -tilting modules via maximal collections of non-crossing tagged generalized permissible curves.
Keywords
Cite
@article{arxiv.2004.11136,
title = {A geometric model for the module category of a skew-gentle algebra},
author = {Ping He and Yu Zhou and Bin Zhu},
journal= {arXiv preprint arXiv:2004.11136},
year = {2023}
}
Comments
Presentation was improved, two tables of notations were added, and a correction for the last condition in the definition of tagged permissible curves was made