| Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W（2, 2） Algebra |
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| 作者姓名： | La Mei YUAN ;Hong YOU |
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| 作者单位： | [1]ScienceResearchCenter,AcademyofFundamentalandInterdisciplinarySciences,HarbinInstituteofTechnology,Harbin150080,P.R.China; [2]ScienceResearchCenter,AcademyofFundamentalandInterdisciplinarySciences,HarbinInstituteofTechnology,Harbin150080,P.R.Chinaand; [3]SchoolofMathematicalSciences,SuzhouUniversity,Suzhou215006,P.R.China |
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| 基金项目： | Supported by China Scholarship Council(Grant No.201206125047);China Postdoctoral Science Foundation Funded Project(Grant No.2012M520715);the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201462) |
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| 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.
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| 关 键 词： | 上同调群 李代数 q变形 低维 一一对应 有限生成 等价类 价值观 |
Low dimensional cohomology of Hom-Lie algebras and q-deformed W(2, 2) algebra |
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| La Mei YUAN,;Hong YOU.Low dimensional cohomology of Hom-Lie algebras and q-deformed W(2, 2) algebra[J].Acta Mathematica Sinica,2014,30(6):1073-1082. |
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| Authors: | La Mei Yuan Hong You |
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| Institution: | 1. Science Research Center, Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin, 150080, P. R. China
2. School of Mathematical Sciences, Suzhou University, Suzhou, 215006, P. R. China
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| Abstract: | 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 α k -derivations and in particular the first cohomology group of the q-deformed W(2, 2) algebra. |
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| Keywords: | Hom-Lie algebras q-deformed W( ) algebra derivation second cohomology group first cohomology group |
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