Isotropic ideals of metric n-Lie algebras

TL;DR

This paper systematically studies isotropic ideals in metric n-Lie algebras, classifies certain low-dimensional cases, and reveals the structure of their centers.

Contribution

It provides a classification of (n+k)-dimensional metric n-Lie algebras with isotropic centers for specific k values.

Findings

Center of non-abelian (n+k)-dimensional metric n-Lie algebra with isotropic center has dimension k-1.

Classified (n+k)-dimensional metric n-Lie algebras for 1< k < n+2.

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.