English

$\tau$-tilting finite gentle algebras are representation-finite

Representation Theory 2019-11-27 v3

Abstract

We show that a gentle algebra over a field is τ\tau-tilting finite if and only if it is representation-finite. The proof relies on the "brick-τ\tau-tilting correspondence" of Demonet-Iyama-Jasso and on a combinatorial analysis.

Keywords

Cite

@article{arxiv.1809.06313,
  title  = {$\tau$-tilting finite gentle algebras are representation-finite},
  author = {Pierre-Guy Plamondon},
  journal= {arXiv preprint arXiv:1809.06313},
  year   = {2019}
}

Comments

7 pages. v2: updated references. v3: Fixed proof of Proposition 3.3