交换环上反对称矩阵李代数的局部导子和2-局部导子

LOCAL DERIVATIONS AND 2-LOCAL DERIVATIONS ON THE LIE ALGEBRA OF ANTISYMMETRIC MATRICES OVER A COMMUTATIVE RING

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.

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).