An Example of Constructing Versal Deformation for Leibniz Algebras

TL;DR

This paper constructs a versal deformation for a specific three-dimensional nilpotent Leibniz algebra over the complex numbers, providing insights into its deformation theory.

Contribution

It explicitly computes a versal deformation for a particular nilpotent Leibniz algebra, advancing understanding of algebraic deformations.

Findings

Computed a versal deformation for the given Leibniz algebra

Identified the deformation parameters and structure

Enhanced understanding of Leibniz algebra deformations

Abstract

In this work we compute a versal deformation of the three dimensional nilpotent Leibniz algebra over $\mathbb{C}$, defined by the nontrivial brackets $[e_1,e_3]=e_2$ and $[e_3,e_3]=e_1$.