On derivations of semisimple Leibniz algebras

TL;DR

This paper characterizes derivations of semisimple Leibniz algebras, showing they can be decomposed into components related to Lie algebra derivations and an explicitly describable part.

Contribution

It provides a novel decomposition of derivations for semisimple Leibniz algebras, extending known results from simple Leibniz algebras.

Findings

Derivations of simple Leibniz algebras decompose into three parts.

A similar decomposition applies to a subclass of semisimple Leibniz algebras.

Explicit descriptions of the third component are provided.

Abstract

In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra derivations and the third one can be explicitly described. Then we show that the similar description can found as well as for a subclass of semisimple Leibniz algebras.