
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 be an Auslander algebra of global dimension equal to 2. We provide a necessary and sufficient condition for to be a tilted algebra. In particular, is tilted if and only if pd.
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