| 量子环面上一类导子李代数的结构和自同构群 |
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| 引用本文： | 陈育明,薛旻,林卫强,谭绍滨.量子环面上一类导子李代数的结构和自同构群[J].数学年刊A辑(中文版),2005(6). |
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| 作者姓名： | 陈育明 薛旻 林卫强 谭绍滨 |
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| 作者单位： | 厦门大学数学科学学院，厦门大学数学科学学院，厦门大学数学科学学院，厦门大学数学科学学院 福建 厦门 361005，福建 厦门 361005，福建 厦门 361005，福建 厦门 361005 |
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| 基金项目： | 国家自然科学基金(No．10371100)
福建省教育厅基金(No．JB04303)
漳州师范学院科研基金(No．SK03003)资助的项目 |
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| 摘 要： | 本文研究量子环面上的一类导子李代数,它包含了Virasoro-Like代数及其q类似．首先证明了这 类导子李代数之间的同构一定是分次同构,并进一步给出了代数同构的充要条件及同构映射的具体表达 式,最后确定了该类李代数的自同构群．
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| 关 键 词： | 李代数 导子 同构 量子环面 |
STRUCTURE AND AUTOMORPHISM GROUP OF A CLASS OF DERIVATION LIE ALGEBRAS OVER QUANTUM TORUS |
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| CHEN Yuming XUE Min LIN Weiqiang TAN Shaobin School of Mathematical Sciences. Xiamen University,Xiamen ,Fujian,China. School of Mathematical Sciences,Xiamen University,Xiamen ,Fujian,China..STRUCTURE AND AUTOMORPHISM GROUP OF A CLASS OF DERIVATION LIE ALGEBRAS OVER QUANTUM TORUS[J].Chinese Annals of Mathematics,2005(6). |
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| Authors: | CHEN Yuming XUE Min LIN Weiqiang TAN Shaobin School of Mathematical Sciences Xiamen University Xiamen Fujian China School of Mathematical Sciences Xiamen University Xiamen Fujian China |
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| Institution: | CHEN Yuming XUE Min LIN Weiqiang TAN Shaobin School of Mathematical Sciences. Xiamen University,Xiamen 361005,Fujian,China. School of Mathematical Sciences,Xiamen University,Xiamen 361005,Fujian,China. |
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| Abstract: | This paper studies a class of derivation Lie algebras over quantum torus, which includes the Virasoro-Like algebra and its q-analog, and proves that every isomorphism between such Lie algebras must be a graded isomorphism. Moreover, the authors give a necessary and sufficient condition for the isomorphic Lie algebras, and obtain the explicit expression of the isomorphisms. Finally, the authors give the structure of the automorphism group of the Lie algebra. |
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| Keywords: | Lie algebra Derivation Isomorphism Quantum torus |
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