Generalized derivation extensions of 3-Lie algebras and corresponding Nambu-Poisson structures

JOURNAL OF GEOMETRY AND PHYSICS

卷:124

Article

Song, Lina¹  Jiang, Jun¹ 

[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China

关键词: 3-Lie algebra;    Leibniz algebra;    Derivation extension;    Matched pair;    Nambu-Poisson structure;   

DOI  :  10.1016/j.geomphys.2017.10.011

来源: Elsevier

【 摘 要 】

In this paper, we introduce the notion of a generalized derivation on a 3-Lie algebra. We construct a new 3-Lie algebra using a generalized derivation and call it the generalized derivation extension. We show that the corresponding Leibniz algebra on the space of fundamental objects is the double of a matched pair of Leibniz algebras. We also determine the corresponding Nambu-Poisson structures under some conditions. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free