The Strong Semi-simple n-Lie Algebras
The Strong Semi-simple n-Lie Algebras
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DOI：
10.1081/agb-120023958
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
R. Bai;Daoji Meng
中科院分区：
文献类型：
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作者：
R. Bai;Daoji Meng
本文定义了强半单n-李代数，并证明了：（1）特征为0的代数闭域F上的有限维n-李代数A是强半单的当且仅当A可分解为其单理想的直和。(2)强半单n-李代数的每个导子都是内导子。(3)强半单n-李代数上的Killing型是非退化的，以及其他性质。
Abstract In this paper, we define the strong semi-simple n-Lie algebra, and prove: (1) A finite dimensional n-Lie algebra A over an algebraically closed field F of characteristic 0 is strong semi-simple if and only if A can be decomposed into the direct sum of its simple ideals. (2) Each derivation of a strong semi-simple n-Lie algebra is inner. (3) The Killing form on a strong semi-simple n-Lie algebra is nondegenerate, and other properties.