An algorithm for the classification of 3-dimensional complex Leibniz algebras

Abstract

We propose an algorithm using Gröbner bases that decides in terms of the existence of a non singular matrix P if two Leibniz algebra structures over a finite dimensional C-vector space are representative of the same isomorphism class.We apply this algorithm in order to obtain a reviewed classification of the 3-dimensional Leibniz algebras given by Ayupov and Omirov. The algorithm has been implemented in a Mathematica notebook.