Auslander algebras which are tilted

TL;DR

This paper characterizes when Auslander algebras of global dimension 2 are tilted, establishing a precise condition involving projective dimension and Auslander-Reiten translation.

Contribution

It provides a necessary and sufficient criterion for Auslander algebras to be tilted, linking homological properties with algebra classification.

Findings

A is tilted if and only if pd(τ_A Ω_A D A) ≤ 1

Characterization of Auslander algebras of global dimension 2 as tilted

Homological condition involving τ_A and Ω_A for tilt-ness

Abstract

Let $A$ be an Auslander algebra of global dimension equal to 2. We provide a necessary and sufficient condition for $A$ to be a tilted algebra. In particular, $A$ is tilted if and only if pd$(\tau_{A}\Omega_{A}DA)\leq1$.