Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W(2, 2) Algebra

被引：0
|
作者：
La Mei YUAN [1 ]
Hong YOU [1 ,2 ]
机构：
[1] Science Research Center, Academy of Fundamental and Interdisciplinary Sciences,Harbin Institute of Technology
[2] School of Mathematical Sciences, Suzhou University
来源：
ActaMathematicaSinica(EnglishSeries) | 2014年 / 30卷 / 06期
基金：
中国博士后科学基金; 中央高校基本科研业务费专项资金资助;
关键词：
Hom-Lie algebras; q-deformed W(2; 2) algebra; derivation; second cohomology group; first cohomology group;
D O I：
暂无
中图分类号：
O154.2 [同调代数];
学科分类号：
0701 ; 070101 ;
摘要：
This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W(2, 2) algebra. We show that the q-deformed W(2, 2) algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W(2, 2) algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W(2, 2) algebra.
引用
收藏
页码：1073 / 1082
页数：10
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