THE STRUCTURE OF SPLIT REGULAR BIHOM-LEIBNIZ COLOR ALGEBRAS

摘要

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 circle plus Sigma([alpha]is an element of Pi/similar to) I-[alpha], with U a subspace of the abelian subalgebra H and any I-[alpha], a well-described ideal of L, satisfying [I-[alpha], I-[beta]] = 0 if [alpha] not equal [beta]. Under certain conditions, in the case of L being of maximal length, the simplicity and the primeness of the algebra is characterized.