Representations and module-extensions of 3-hom-Lie algebras

被引：14

作者：

Liu, Yan ^{[1
]}

Chen, Liangyun ^{[1
]}

Ma, Yao ^{[2
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2015年 / 98卷

基金：

中国国家自然科学基金;

关键词：

3-hom-Lie algebra; Module-extension; T-theta-extension; T-theta*-extension; Representation;

D O I：

10.1016/j.geomphys.2015.08.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the representations and module-extensions of 3-hom-Lie algebras. We show that a linear map between 3-hom-Lie algebras is a morphism if and only if its graph is a horn subalgebra and show that the set of derivations of a 3-hom-Lie algebra is a Lie algebra. Moreover, we introduce the definition of To-extensions and 4-extensions of 3-hom-Lie algebras in terms of modules, providing the necessary and sufficient conditions for a 2k-dimensional metric 3-hom-Lie algebra to be isometric to a 4-extension. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：376 / 383

页数：8

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