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

作     者：La Mei YUAN Hong YOU 

作者机构：Science Research Center Academy of Fundamental and Interdisciplinary SciencesHarbin Institute of Technology School of Mathematical Sciences Suzhou University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第6期

页      面：1073-1082页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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) 

主　　题：Hom-Lie algebras q-deformed W(2 2) algebra derivation second cohomology group first cohomology group 

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 *** application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.