Leibniz algebras whose solvable ideal is the maximal extension of the nilradical

TL;DR

This paper investigates a class of Leibniz algebras with complete ideals, proving that such algebras are split when the ideal is solvable and related to the nilradical's generators.

Contribution

It extends known results about Lie algebras to Leibniz algebras, establishing conditions under which these algebras are split.

Findings

Leibniz algebras with complete solvable ideals are split under specified conditions.

The codimension of the nilradical equals the number of generators in these algebras.

Generalizes the split property from Lie to Leibniz algebras.

Abstract

The paper is devoted to the so-called complete Leibniz algebras. It is known that a Lie algebra with a complete ideal is split. We will prove that this result is valid for Leibniz algebras whose complete ideal is a solvable algebra such that the codimension of nilradical is equal to the number of generators of the nilradical.