Poincaré–Birkhoff–Witt Theorem for Quadratic Algebras of Koszul Type Original Research Article

In this paper we prove a general Poincaré–Birkhoff–Witt theorem for quadratic Koszul algebras. The result is similar to that obtained by Polischuk and Positselsky, but the proof is entirely different and uses algebraic deformation theory. In particular, we obtain a new proof of the classical PBW-theorem for Lie algebras, based on deformation theory.