Isotropic ideals of metric n-Lie algebras

Abstract

In this paper, we give a systematic study on isotropic ideals of metric n-Lie algebras. As an application, we show that the center of a non-abelian (n+k)-dimensional metric n-Lie algebra (1< k< n+2), whose center is isotropic, is of dimension k-1. Furthermore, we classify (n+k)-dimensional metric n-Lie algebras for 1< k < n+2.