TITLE:
On Two Classes of Extended 3-Lie Algebras
AUTHORS:
Yu Cheng, Yansha Gao
KEYWORDS:
The Unary Extension 3-Lie Algebras, Lie Algebra, (μ, ρ, β)-Extension
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.4,
April
30,
2021
ABSTRACT: In this paper, based on the existing research results, we obtain the unary extension 3-Lie algebras by one-dimensional extension of the known Lie algebra L. For two known 3-Lie algebras H, M, the (μ, ρ, β)-extension of H through M is given, and the necessary and sufficient conditions for the (μ, ρ, β)-extension algebra of H through M being 3-Lie algebra are obtained, and the structural characteristics and properties of these two kinds of extended 3-Lie algebras are given.