The Classification of n-Lie Algebras

TL;DR

This paper provides a complete classification of low-dimensional n-Lie algebras over algebraically closed fields of characteristic zero, including criteria for isomorphism and explicit classifications for dimensions n+1 and n+2.

Contribution

It establishes an isomorphic criterion theorem and classifies (n+1)- and (n+2)-dimensional n-Lie algebras over algebraically closed fields of characteristic zero.

Findings

Proved the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras.

Provided a complete classification of (n+1)-dimensional n-Lie algebras.

Provided a complete classification of (n+2)-dimensional n-Lie algebras.

Abstract

This paper proves the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras, and gives a complete classification of (n+1)-dimensional n-Lie algebras and (n+2)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero.