Mathematica Eterna
Open Access

Abstract

3-Lie algebra A with I(A) = 3, 4 I

BAI Ruipu, ZHANG Yinghua, and GAO Yansha

The paper introduces the symplectic structure on 3-Lie algebras. And it is proved that: 1) The simple 3-Lie algebra is a metric symplectic 3-Lie algebra. 2). There does not exist metric structure on the nonsimple and non-abelian 3-Lie algebra A with the generating index three and four. 3). Except for the cases of abelian and (a4), there does not exist symplectic structure on the non-simple 3-Lie algebra A with the generating index three and four.