English

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 τ\tau-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