The structure of split regular Hom-Leibniz–Poisson color algebras

Abstract

In this paper, we introduce the class of split regular Hom-Leibniz–Poisson color algebras as the natural generalization of split regular Hom-Leibniz algebras, split regular Hom-Poisson algebras and split regular Hom-Leibniz–Poisson superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz–Poisson color algebra [Formula: see text] is of the form [Formula: see text] with [Formula: see text] a subspace of the abelian sub algebra [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 and the primeness of the algebra is characterized and it is shown that [Formula: see text] is the direct sum of the family of its minimal ideals, each one being a simple split regular Hom-Leibniz–Poisson color algebra.