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

作　　者：La Mei YUAN Hong YOU 

机构地区：[1]Science Research Center, Academy of Fundamental and Interdisciplinary Sciences,Harbin Institute of Technology [2]School of Mathematical Sciences, Suzhou University

出　　处：《Acta Mathematica Sinica,English Series》2014年第6期1073-1082,共10页数学学报（英文版）

基　　金：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)

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.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.

关 键 词：Hom-Lie algebras q-deformed W（2 2） algebra DERIVATION second cohomology group first cohomology group 

分 类 号：O154.2[理学—数学]