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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.