Noncommutative Auslander theorem

TL;DR

This paper extends the Auslander theorem to various classes of noncommutative algebras, including noetherian PI local algebras, universal enveloping algebras, and graded down-up algebras, revealing new structural insights.

Contribution

It proves a version of the Auslander theorem for specific noncommutative algebra classes, broadening its applicability beyond classical settings.

Findings

Auslander theorem holds for noetherian PI local algebras of finite injective dimension

Universal enveloping algebras of finite dimensional Lie algebras satisfy the theorem

Noetherian graded down-up algebras also conform to the theorem

Abstract

A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie algebras, and (c) noetherian graded down-up algebras.