The Poincare-Birkhoff-Witt theorem for quadratic algebras of Koszul type
  In this paper we discuss a generalization of the classica PBW-theorem to the case of Koszul algebras. Our result is a slight generalization of that obtained by A.Polischuk and L.Positselsky, but the proof is different and uses deformation theory. 
Alexander Braverman and Dennis Gaitsgory