Another characterization of tilted algebras

TL;DR

This paper introduces a new way to identify tilted algebras by examining specific subquivers in their Auslander-Reiten quiver, expanding existing characterizations and enabling the construction of more tilted quotient algebras.

Contribution

It provides a novel characterization of tilted algebras based on special subquivers, enhancing understanding and construction methods.

Findings

New characterization of tilted algebras via subquivers

Includes previous characterizations as special cases

Provides a method to generate more tilted quotient algebras

Abstract

We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted quotient algebras from a given algebra.