Constructing (n + 1)-Lie algebras from n-Lie algebras

Abstract

n-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. In this paper, we construct (n + 1)-Lie algebras by two-dimensional extensions of metric n-Lie algebras, and construct (n + 1)-Lie algebras in terms of n-Lie algebras and certain linear functions. Along this approach, we obtain (n + 1)-Lie algebras by n-Lie algebras with the generating index n, and 4-Lie algebras by non-nilpotent 3-Lie algebras with the generating index 4.