AI 中文总结
该研究对约化李代数上的模值2-局部导子分类，得出其为导子的充要条件，以及特定情形下例外2-局部导子的构成。
AI 中文摘要
设𝔽是特征为零的代数闭域，𝔤=𝔰⊕𝔷是𝔽上的有限维约化李代数，V是任意有限维𝔤-模。我们对𝔤在V上的所有2-局部导子进行分类，证明每个2-局部导子都是导子当且仅当dim𝔷≤1或V^𝔤=0；若dim𝔷≥2且V^𝔤≠0，则非线性齐次映射构成所有例外2-局部导子。
英文摘要
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.
