On split regular BiHom-Lie superalgebras

Abstract

Abstract 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.