On Low Dimensional Leibniz Algebras

Abstract

Leibniz algebras are generalization of Lie algebras. In literature, there are many studies on one dimensional and two dimensional Leibniz algebras. The structure of three dimensional Leibniz algebras are more complicated than the structure of one dimensional and two dimensional Leibniz algebras. In this study, our main aim is to investigate three dimensional non-Lie Leibniz algebras. Moreover, we prove that for any three dimensional non-Lie Leibniz algebra L, there exists at least one Leibniz algebra which is isomorphic to...... DOI : 10.7176/JSTR/5-2-15