Isotopism Classes of 2-dimensional Leibniz Algebras

Abstract

This paper gives the classification of two-dimensional Leibniz algebras into isotopism classes. The matrix structure constants of the algebras were used to determine the isotopism between them. An algorithm was developed for n-dimensional Leibniz to achieve this objective. The  algorithm was tested on the Leibniz algebras of dimension two over Z2. From the result obtained, it was observed that there is no isotopism between the algebras. Consequently, we conclude that isotopism and isomorphism are equivalent in this case.