On split regular BiHom-Lie superalgebras

We introduce the class of split regular BiHom-Lie superalgebras as the natural extension of the one of split Hom-Lie superalgebras and the one of split Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Lie superalgebra L is of the form L=U+∑[α]∈Λ∕∼I[α] with U a subspace of the Abelian (graded) subalgebra H and any I[α], a well described (graded) 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 of the algebra is characterized and it is shown that L is the direct sum of the family of its simple (graded) ideals.