Leibniz algebra deformations of a Lie algebra

Abstract

In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra ${\mathfrak{n}}_3$ and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of ${\mathfrak{n}}_3$ with the versal base.

15 pages