Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

We study the invariants \(\alpha \) $\alpha$ and \(\beta \) $\beta$ , which correspond to the dimension of an abelian subalgebra (ideal resp.) of maximal dimension, in the context of Leibniz superalgebras. We prove that these invariants coincide if there is an abelian subalgebra of codimension one. We also examine the case in which the abelian subalgebras of maximal dimension are of codimension two. Finally, we study the \(\alpha \) $\alpha$ and \(\beta \) $\beta$ invariants for some distinguished families of Leibniz superalgebras.