Constructions Of Metric N-lie Algebra

We study the structure of a metric n-Lie algebra g over the complex field C. Let g= S⊕R be the Levi decomposition, where R is the radical of g and S is a strong semisimple subalgebra of g. Denote by m(g) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R⊥the orthogonal complement of R.We obtain the following results:1. Given some property about isotropic ideal of metric n-lie algebra.2. We show that the center of a non-abelian (n+k)-dimensional metric n-Lie algebra (2≤k<≤n+1), whose center is isotropic. We classify (n+k)-dimensional metric n-Lie algebras for 2<≤k≤n+1.3. The dimension of metric n-lie algebra is greater than or equal to m(g)+1.4. As S-modules, levi factor is isomorphic to the R⊥5. The dimension of the vector space spanned by all nondegenerate invariant sym-metric bilinear forms on g equals that of the vector space of certain linear transformations on g.