On split regular Hoin-Leibniz algebras

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Horn-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Horn- Leibniz algebra L is of the form L = U + Sigma([j]is an element of Lambda/similar to)I([j] )with U a subspace of the abelian subalgebra H and any III, a well described ideal of L, satisfying [I[j], I[k]] = 0 if [j] not equal [k]. Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized.