关键词: 半单, 可解, 非退化

Abstract: The authors make a definition of non-degeneracy for the killing form of an n-Lie algebra and prove that an n-Lie algebra is semisimple if and only if its killing form is non-degenerate.The authors also give an example which sho ws that a semisimple n-Lie algebra need not to be a direct sum of simple ideals.