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

Abstract

In this paper, we establish a converse to Schur's theorem for Lie superalgebras \( L \), focusing on cases where the minimal generator number pairs \((p \vert q)\) of \( L/Z(L) \) are considered, and where the superdimension \( \mathrm{sdim} L^{2} \) 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 \( st(L) \in \{(0,0), (1,0), (0,1), (2,0), (0,2), (1,1)\} \).

We have made some modifications to the paper. Specifically, certain sections have been revised to enhance clarity and strengthen the overall argument. Additionally, improvements have been made to the abstract to better summarize the key findings and contributions of the paper