有限维单李代数的2-局部导子

赖璇, 陈正新

数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 847-852.

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PDF(396 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 847-852. DOI: 10.12386/A2015sxxb0084
论文

有限维单李代数的2-局部导子

    赖璇, 陈正新
作者信息 +

2-Local Derivations of Finite-Dimensional Simple Lie Algebras

    Xuan LAI, Zheng Xin CHEN
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文章历史 +

摘要

F 是特征为零的代数封闭域, gF 上有限维单李代数. g 上的一个映射 φ 称为 2-局部导子, 如果对任意的 x, yg, 存在导子 Dx, y: gg, 使 φ(x) = Dx, y(x), φ(y) = Dx, y(y). 本文证明 g 上的所有 2-局部导子一定是内导子.

Abstract

Let F be an algebraically closed field of characteristic 0, g a finite-dimensional simple Lie algebra over F. Amap φ on g is called a 2-local derivation, if for any x, yg, there is a derivation Dx, y: gg, such that φ(x)=Dx, y(x), φ(y)=Dx, y(y). We prove that any 2-local derivation of g is an inner derivation.

关键词

2-局部导子 / 内导子 / 有限维单李代数

Key words

2-local derivation / inner derivation / finite-dimensional simple Lie algebra

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赖璇, 陈正新. 有限维单李代数的2-局部导子. 数学学报, 2015, 58(5): 847-852 https://doi.org/10.12386/A2015sxxb0084
Xuan LAI, Zheng Xin CHEN. 2-Local Derivations of Finite-Dimensional Simple Lie Algebras. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 847-852 https://doi.org/10.12386/A2015sxxb0084

参考文献

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基金

国家自然科学基金资助项目(11101084);福建省自然科学基金资助项目(2013J01005)

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