Singularity categories of gentle algebras
Representation Theory
2015-06-12 v3 Rings and Algebras
Abstract
We determine the singularity category of an arbitrary finite dimensional gentle algebra . It is a finite product of -cluster categories of type . Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If is a Jacobian algebra arising from a triangulation of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of .
Keywords
Cite
@article{arxiv.1207.6941,
title = {Singularity categories of gentle algebras},
author = {Martin Kalck},
journal= {arXiv preprint arXiv:1207.6941},
year = {2015}
}
Comments
11 pages; minor changes, final version, to appear Bulletin of the LMS