On split regular Hom-Leibniz algebras

Abstract

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz algebra [Formula: see text] is of the form [Formula: see text] with [Formula: see text] a subspace of the abelian subalgebra [Formula: see text] and any [Formula: see text], a well described ideal of [Formula: see text], satisfying [Formula: see text] if [Formula: see text]. Under certain conditions, in the case of [Formula: see text] being of maximal length, the simplicity of the algebra is characterized.