| q-Deformation of W（2, 2） Lie Algebra Associated with Quantum Groups |
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| 作者姓名： | La Mei YUAN |
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| 作者单位： | [1]Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150080, P. R. China [2]Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant No. 10825101） |
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| 摘 要： | The q-deformation of W (2, 2) Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W (2, 2) Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W (2, 2) Lie algebra is studied, which turns out to be coincided with the conventional W (2, 2) Lie algebra in the q → 1 limit.
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| 关 键 词： | 李代数 q变形 量子群 关联 Lie代数 中心扩张 振荡器 费米子 |
q-deformation of W (2, 2) Lie algebra associated with quantum groups |
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| La,Mei,YUAN.q-deformation of W (2, 2) Lie algebra associated with quantum groups[J].Acta Mathematica Sinica,2012,28(11):2213-2226. |
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| Authors: | La Mei Yuan |
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| Institution: | 1. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin, 150080, P. R. China
2. Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, 230026, P. R. China
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| Abstract: | The q-deformation of W (2, 2) Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W (2, 2) Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W (2, 2) Lie algebra is studied, which turns out to be coincided with the conventional W (2, 2) Lie algebra in the q → 1 limit. |
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| Keywords: | W（2 2） Lie algebra q-deformation quantum group central extension |
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