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arXiv · 2608.20681

Module-Valued 2-Local Derivations on Reductive Lie Algebras

Yang Chen·Yongqi Luo·Junzi Xu
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Abstract

Let \(\F\) be an algebraically closed field of characteristic zero, \(\g=\s\oplus\z\) a finite-dimensional reductive Lie algebra over \(\F\), and \(V\) an arbitrary finite-dimensional \(\g\)-module. We classify all 2-local derivations of \(\g\) on \(V\), and show that every 2-local derivation is a derivation if and only if \(\dim\z\leq1\) or \(V^\g=0\). If \(\dim\z\geq2\) and \(V^\g\ne0\), the nonlinear homogeneous maps give all exceptional 2-local derivations.

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Yang Chen, Yongqi Luo, Junzi Xu. 2026-08-21. Module-Valued 2-Local Derivations on Reductive Lie Algebras. https://arxiv.org/abs/2608.20681

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