Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

Xiaohui Chi; Huiyi Zhang; Lingxin Meng; Liming Tang

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

Rings and Algebras 2026-07-01 v1

Authors: Xiaohui Chi , Huiyi Zhang , Lingxin Meng , Liming Tang

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.

Keywords

local superderivations nilpotent Lie superalgebras pure local superderivations anti-superderivations

Cite

@article{arxiv.2607.00393,
  title  = {Local (Anti-)Superderivations on Nilpotent Lie Superalgebras},
  author = {Xiaohui Chi and Huiyi Zhang and Lingxin Meng and Liming Tang},
  journal= {arXiv preprint arXiv:2607.00393},
  year   = {2026}
}