On a class of Leibniz Algebras

TL;DR

This paper investigates a specific class of Leibniz algebras and establishes that if their Killing form is non-degenerate, then these algebras are semisimple, extending classical Lie algebra results.

Contribution

It identifies a class of Leibniz algebras where non-degenerate Killing form guarantees semisimplicity, generalizing known properties from Lie algebras.

Findings

Non-degenerate Killing form implies semisimplicity in this class

Extension of classical Lie algebra results to Leibniz algebras

Characterization of Leibniz algebras with non-degenerate Killing form

Abstract

We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebra is semisimple.