设 F 是特征为零的代数封闭域, g 为 F 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, y ∈ g, 存在导子 Dx, y: g→g, 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, y ∈ g, there is a derivation Dx, y: g→g, 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
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Key words
2-local derivation /
inner derivation /
finite-dimensional simple Lie algebra
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参考文献
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脚注
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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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