Classifications of (n plus k)-dimensional metric n-Lie algebras

We study the structure of isotropic ideals of the metric n-Lie algebra (g, B) over the complex field C for n >= 2. Based on the study of isotropic ideals of metric n-Lie algebras in this paper, we obtain the following. (i) Let g = s circle plus r be the Levi decomposition and g without semi-simple ideals. If n > 2, g is perfect and r is isotropic, then r is the unique isomaximal ideal and dim g = 2m(n + 1), and the metric dimension of g is m. If g is indecomposable, then r is isomorphic to s as an s-module in the regular representation. (ii) If dim g = n + k with 2 <= k <= n + 1, then dim g(1) <= n + k - 1. If g is unsolvable, then g is reductive. If the center C(tau) of g is isotropic, then dimC(tau) = k - 1. (iii) There are only three classes of (n + k)-dimensional metric n-Lie algebras for 2 <= k <= n + 1 and n > 2, and the concrete multiplications for each class are provided.