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arXiv · 2607.00393

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

Xiaohui Chi·Huiyi Zhang·Lingxin Meng·Liming Tang
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Abstract

In this paper, we study local (anti-)superderivations on finite-dimensional nilpotent Lie superalgebras. Firstly, we prove that every finite-dimensional 2-step nilpotent Lie superalgebra over a field $\mathbb{F}$ with $\operatorname{char}\mathbb{F}\neq2$ admits pure local (anti-)superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). Then for $n$-step nilpotent Lie superalgebras over arbitrary fields with n greater than 2, we provide a sufficient criterion to guarantee the existence of pure local (anti-)superderivations. Furthermore, we show that 3-step nilpotent Lie superalgebras admit pure localsuperderivations.

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Xiaohui Chi, Huiyi Zhang, Lingxin Meng, Liming Tang. 2026-07-01. Local (Anti-)Superderivations on Nilpotent Lie Superalgebras. https://arxiv.org/abs/2607.00393

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