Detecting capable pairs of some nilpotent Lie superalgebras

In this article, we define the capable pairs of Lie superalgebras. We classify all capable pairs of abelian and Heisenberg Lie superalgebras. After that we discuss on pairs of Lie superalgebras with derived subalgebra of dimension one and a non-abelian ideal. Finally, we determine the structure of the Schur multiplier of pairs of Heisenberg Lie superalgebras.