PBW-deformations and deformations `a la Gerstenhaber of N-Koszul algebras

In this article we establish an explicit link between the classical theory of deformations `a la Gerstenhaber – and a fortiori with the Hochschild cohomology– and (weak) PBW-deformations of homogeneous algebras. Our point of view is of cohomological nature. As a consequence, we recover a theorem by R. Berger and V. Ginzburg, which gives a precise condition for a filtered algebra to satisfy the so-called PBW property, under certain assumptions.