Journal of Noncommutative Geometry


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Volume 8, Issue 2, 2014, pp. 505–539
DOI: 10.4171/JNCG/163

Published online: 2014-07-18

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

Estanislao Herscovich[1], Andrea Solotar[2] and Mariano Suárez-Álvarez[3]

(1) Bielefeld University, Germany
(2) Universidad de Buenos Aires, Argentina
(3) Universidad de Buenos Aires, Argentina

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.

Keywords: Deformation theory, Koszul algebras, Hochschild cohomology

Herscovich Estanislao, Solotar Andrea, Suárez-Álvarez Mariano: PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras. J. Noncommut. Geom. 8 (2014), 505-539. doi: 10.4171/JNCG/163