On split regular BiHom-Leibniz superalgebras

The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Leiniz superalgebras $mathfrak{L}$ is of the form $mathfrak{L}=U+sum_{a}I_a$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{a}$, a well described ideal of $mathfrak{L}$, satisfying $[I_a, I_b]= 0$ if $[a] eq [b]$. In the case of $mathfrak{L}$ being of maximal length, the simplicity of $mathfrak{L}$ is also characterized in terms of connections of roots.