In this article we establish an explicit link between the classical theory of deformations à 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.
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Estanislao Herscovich, Andrea Solotar, Mariano Suárez-Álvarez, PBW-deformations and deformations à la Gerstenhaber of <var>N</var>-Koszul algebras. J. Noncommut. Geom. 8 (2014), no. 2, pp. 505–539