English

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 Λ\Lambda. It is a finite product of nn-cluster categories of type A1\mathbb{A}_{1}. Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If Λ\Lambda is a Jacobian algebra arising from a triangulation \ct\ct of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of \ct\ct.

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