The structure of split regular BiHom-Leibniz color algebras

Abstract

We introduce the class of split regular BiHom-Leibniz color algebras as the natural generalization of split regular Hom-Leibniz algebras. By developing techniques of connections of roots for this kind of algebra, we show that such a split regular BiHom-Leibniz color algebra ℒ is of the form ℒ=𝒰⊕∑[α]∈Π∕∼I[α], with 𝒰 a subspace of the abelian subalgebra ℋ and any I[α], a well-described ideal of ℒ, satisfying [I[α],I[β]]=0 if [α]≠[β]. Under certain conditions, in the case of ℒ being of maximal length, the simplicity and the primeness of the algebra is characterized.