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. 
Estanislao Herscovich, Andrea Solotar and Mariano Su\'arez-\'Alvarez
math.KT math.RA