Central extensions and deformations of Hom-Lie triple systems

被引：13
作者：
Ma, Yao [1 ]
Chen, Liangyun [1 ]
Lin, Jie [2 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
[2] Civil Aviat Univ China, Sinoeuropean Inst Aviat Engn, Tianjin, Peoples R China
来源：
COMMUNICATIONS IN ALGEBRA | 2018年 / 46卷 / 03期
基金：
中国博士后科学基金;
关键词：
Central extension; cohomology; deformation; Hom-Lie triple system; ALGEBRAS; RINGS; COHOMOLOGY; REPRESENTATIONS; NAMBU;
D O I：
10.1080/00927872.2017.1339063
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the cohomology theory of Horn-Lie triple systems generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce the central extension theory for Horn-Lie triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Hom-Lie triple systems and the third cohomology group. We develop the 1-parameter formal deformation theory of Horn-Lie triple systems and prove that it is governed by the cohomology group.
引用
收藏
页码：1212 / 1230
页数：19
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