| 摘要: |
| 令R是有单位元1的2-挠自由交换环，Ln（R）是由R上所有n阶反对称矩阵构成的李代数.本文研究了Ln（R）（n≥3）上局部导子和2-局部导子的性质.利用Ln（R）作为李代数的完备性和矩阵计算技巧，证明了Ln（R）上的每个局部导子和2-局部导子都是导子.推广了Ln（R）上关于导子的主要结果. |
| 关键词: 导子 局部导子 2-局部导子 反对称矩阵李代数 交换环 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:国家自然科学基金资助（11471090）. |
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| LOCAL DERIVATIONS AND 2-LOCAL DERIVATIONS ON THE LIE ALGEBRA OF ANTISYMMETRIC MATRICES OVER A COMMUTATIVE RING |
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WANG Di, WANG Yin
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School of Mathematical Sciences, Dalian University of Technology, Dalian 116024
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| Abstract: |
| Let R be a 2-torsion free commutative ring with identity 1 and Ln(R) a Lie algebra consisting of all n×n antisymmetric matrices over R. The aim of this paper is to study the character of the local derivations and 2-local derivations of Ln(R). By using that Ln(R) is a complete Lie algebra and the skill of matrix computation, it is proved that every local derivation and every 2-local derivation of Ln(R) are derivations, which extends the main result of derivations of Ln(R). |
| Key words: derivation local derivation 2-local derivation Lie algebra of antisymmetric matrices commutative ring |
