PBW-deformations and deformation à la Gerstenhaber of N-Koszul algebras.

HERSCOVICH, ESTANISLAO; SOLOTAR, ANDREA; SUAREZ-ALVAREZ, MARIANO

JOURNAL OF NONCOMMUTATIVE GEOMETRY

EUROPEAN MATHEMATICAL SOC

Lugar: Zürich; Año: 2014 vol. 8 p. 505 - 539

1661-6952

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.