Some Theorems on Leibniz n-Algebras from the Category Un (Lb)

Abstract

We study the Leibniz [Formula: see text]-algebra [Formula: see text], whose multiplication is defined via the bracket of a Leibniz algebra [Formula: see text] as [Formula: see text]. We show that [Formula: see text] is simple if and only if [Formula: see text] is a simple Lie algebra. An analog of Levi's theorem for Leibniz algebras in [Formula: see text] is established and it is proven that the Leibniz [Formula: see text]-kernel of [Formula: see text] for any semisimple Leibniz algebra [Formula: see text] is the [Formula: see text]-algebra [Formula: see text].