| 量子环面的收缩李代数及其导子和泛中心扩张 |
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| 引用本文： | 郑志明,林卫强.量子环面的收缩李代数及其导子和泛中心扩张[J].漳州师院学报,2012(2):9-17. |
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| 作者姓名： | 郑志明 林卫强 |
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| 作者单位： | 漳州师范学院数学与信息科学系,漳州福建363000 |
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| 基金项目： | 国家自然科学基金资助项目（11171294）;福建省教育厅新世纪人才计划资助项目 |
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| 摘 要： | 本文利用收缩（contraction）的方法由两个变量的量子环面构造出一个新的无穷维李代数，并对它进行了研究．本文第一部分研究了这个李代数的结构，并证明它可看成Virasoro-like代数的一种-AbeI扩张．第二部分首先证明了这个李代数是有限生成的，进而研究了它的导子并确定了它的所有导子．最后一部分，通过计算它的二上圈（2-cocycle）进而确定了它的泛中心扩张．
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| 关 键 词： | 收缩 量子环面 Virasoro-like代数 导子 泛中心扩张 |
A Contraction Lie Algebra of Quantum Torus and its Derivations and Universal Central Extension |
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| ZHENG Zhi-ming,LIN Wei-qiang.A Contraction Lie Algebra of Quantum Torus and its Derivations and Universal Central Extension[J].Journal of ZhangZhou Teachers College(Philosophy & Social Sciences),2012(2):9-17. |
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| Authors: | ZHENG Zhi-ming LIN Wei-qiang |
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| Institution: | (Department of Mathematics and Information Science,Zhangzhou Normal University, Zhangzhou, Fujian 363000,China) |
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| Abstract: | In this paper a new infinite dimensional Lie algebra is constructed from two variable quantum tori by using the contraction technique, and it is proved that Lie algebra can be seen as an Abel extension of Virasoro-like algebra. Then it is attested that Lie algebra is finitely generated and all of its derivations are determined. Its universal central extension is eventually determined through calculating its 2-cocycle. |
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| Keywords: | contraction Lie algebra quantum torns Virasoro-like algebra derivations universal centralextension |
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