There are no strictly shod algebras in hereditary gentle algebras

Abstract

We prove that there are no strictly shod algebras in hereditary gentle algebras by geometric models. As an application, we give a classification of the silted algebras for Dynkin type ${\mathbb{A}}_n$ and ${\tilde{\mathbb{A}}}_n$.

arXiv comment14 pages, v2: minor corrections, to appear in Communications in Algebra