Low dimensional cohomology of Hom-Lie algebras and q-deformed W(2, 2) algebra

被引：0
作者：
La Mei Yuan
Hong You
机构：
[1] Harbin Institute of Technology,Science Research Center, Academy of Fundamental and Interdisciplinary Sciences
[2] Suzhou University,School of Mathematical Sciences
来源：
Acta Mathematica Sinica, English Series | 2014年 / 30卷
关键词：
Hom-Lie algebras; -deformed ; (2,2) algebra; derivation; second cohomology group; first cohomology group; 17A30; 17A60; 17B68; 17B70;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper aims to study low dimensional cohomology of Hom-Lie algebras and the q-deformed 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.
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页码：1073 / 1082
页数：9
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