ON THE STRUCTURE CONSTANTS OF LEIBNIZ ALGEBRAS

Abstract: Leibniz algebras are generalization of Lie algebras. As an immediate consequence, every Lie algebras are Leibniz algebras. In literature, there are many papers on finite dimensional Leibniz algebras.In this note, our main goal is to focus on the structure constants of Leibniz algebras and to give some properties of the structure constants of Leibniz algebras. In particular, some conditions are investigated for non-Lie Leibniz algebras. Moreover, some examples on structure constants of non-Lie Leibniz algebras are given and the structure constants of Leibniz kernel of a Leibniz algebra is investigated.

Keywords: Leibniz algebra, Lie algebra, structure constants, Leibniz kernel ideal.