On the Schur multiplier of nilpotent Lie superalgebra

Let L be an (m n)-dimensional nilpotent Lie superalgebra where m + n ≥ 4 and n ≥ 1. This paper classifies such nilpotent Lie superalgebras L with a derived subsuperalgebra of dimension $m+n-2$ such that γ(L) = m + 2n - 2 - M(L), where γ(L) ∈ \0, 1, 2\ and M(L) denotes the Schur multiplier of L. Furthermore, we show that all these superalgebras are capable.