On converse of the Schur's theorem for nilpotent Lie superalgebras

In this paper, we establish a converse to Schur’s theorem for Lie superalgebras $L$, focusing on cases where the minimal generator number pairs $(p\mathrm{\mid }q)$ of $L\mathrm{/}Z(L)$ are considered, and where the superdimension $\mathrm{s}\mathrm{d}\mathrm{i}\mathrm{m}{L}^2$ is finite. We introduce a new invariant $st(L)$, which plays a key role in the classification of finite-dimensional nilpotent Lie superalgebras. Specifically, we classify the structure of all such Lie superalgebras $L$ when $st(L)\in \{(0,0),(1,0),(0,1),(2,0),(0,2),(1,1)\}$.