Mathematica Eterna
Open Access

Abstract

A class of 3-Lie algebras realized by Lie algebras

BAI Ruipu, GAO Yansha and GUO Weiwei

The structure of 3-Lie algebra G which is constructed by one dimensional extension of Lie algebra L is studied. Let L be a Lie algebra, then G = L ⊕ F x0 is a 3-Lie algebra with the multiplication (1.1) given below. It is proved that for I ⊆ L is an ideal of L if and only if I is an ideal of 3-Lie algebra G, and G is 2-solvable if and only if L is a solvable Lie algebra. The derivations and inner derivations of G are described by means of derivations of L.