English

On total stability conditions for Dynkin quivers

Representation Theory 2022-05-03 v1

Abstract

We show that for a Dynkin quiver QQ of type E7E_7 with a specific orientation, the path algebra KQKQ has no slope function of the form μ=θdim\mu=\frac{\theta}{\dim} that defines a total stability condition. This gives a counterexample to a conjecture of Reineke.

Cite

@article{arxiv.2205.00947,
  title  = {On total stability conditions for Dynkin quivers},
  author = {Rene Marczinzik},
  journal= {arXiv preprint arXiv:2205.00947},
  year   = {2022}
}
R2 v1 2026-06-24T11:04:50.863Z