Noncommutative Auslander theorem
  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. 
Y.-H. Bao, J.-W. He and J. J. Zhang
math.RA