Abelian extensions of Lie triple systems with derivations

被引：5
作者：
Wu, Xueru [1 ]
Ma, Yao [1 ]
Chen, Liangyun [1 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
来源：
ELECTRONIC RESEARCH ARCHIVE | 2022年 / 30卷 / 03期
关键词：
Lie triple system; cohomology; derivation; abelian extension; COHOMOLOGIES;
D O I：
10.3934/era.2022058
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let .2 and A be Lie triple systems, and let theta A be a representation of .2 on A. We first construct the third-order cohomology classes by derivations of A and .2, then obtain a Lie algebra G theta A with a representation 0 on H3(.2, A), where theta A is given by an abelian extension 0 // A //.2 tilde pi // .2 // 0 . We study obstruction classes for extensibility of derivations of A and .2 to those of .2 tilde . An application of 0 is discussed.
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页码：1087 / 1103
页数：17
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