On split regular Hom-Lie superalgebras

We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra L is of the form L=U+∑jIj with U a linear subspace of a maximal abelian graded subalgebra H and any Ij a well described (split) ideal of L satisfying [Ij,Ik]=0 if j≠k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its simple ideals.