There are no strictly shod algebras in hereditary gentle algebras

TL;DR

This paper proves that strictly shod algebras do not exist within hereditary gentle algebras using geometric models, and classifies silted algebras for certain Dynkin types.

Contribution

It establishes the non-existence of strictly shod algebras in hereditary gentle algebras and classifies silted algebras for specific Dynkin types.

Findings

No strictly shod algebras in hereditary gentle algebras

Classification of silted algebras for Dynkin type A_n

Classification of silted algebras for affine type Ã_n

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 $\widetilde{\mathbb{A}}_{n}$.