Low Dimensional Cohomology of Hom-Lie Algebras and 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-Li...
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| Veröffentlicht in: | 数学学报：英文版 2014 (6), p.1073-1082 |
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| container_title | 数学学报：英文版 |
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| creator | La Mei YUAN Hong YOU |
| description | 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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| ispartof | 数学学报：英文版, 2014 (6), p.1073-1082 |
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| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | q变形 一一对应 上同调群 价值观 低维 有限生成 李代数 等价类 |
| title | Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W（2, 2） Algebra |
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