| Lie bialgebras of generalized Witt type |
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| 引用本文： | SONG Guang''''ai & SU Yucai College of Mathematics and Information Science,Shandong Institute of Business and Technology,Yantai 264005,China, Department of Mathematics,University of Science and Technology of China,Hefei 230026,China, Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China. Lie bialgebras of generalized Witt type[J]. 中国科学A辑(英文版), 2006, 49(4): 533-544. DOI: 10.1007/s11425-006-0533-7 |
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| 作者姓名： | SONG Guang''''ai & SU Yucai College of Mathematics and Information Science Shandong Institute of Business and Technology Yantai 264005 China Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China |
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| 作者单位： | SONG Guang'ai & SU Yucai College of Mathematics and Information Science，Shandong Institute of Business and Technology，Yantai 264005，China; Department of Mathematics，University of Science and Technology of China，Hefei 230026，China; Department of Mathematics，Shanghai Jiaotong University，Shanghai 200240，China |
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| 摘 要： | In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.
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| 收稿时间： | 2005-02-21 |
| 修稿时间： | 2005-09-19 |
Lie bialgebras of generalized Witt type |
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| SONG Guang'ai,SU Yucai. Lie bialgebras of generalized Witt type[J]. Science in China(Mathematics), 2006, 49(4): 533-544. DOI: 10.1007/s11425-006-0533-7 |
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| Authors: | SONG Guang'ai SU Yucai |
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| Affiliation: | 1. College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, China;Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
2. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China;Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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| Abstract: | In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial. |
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| Keywords: | Lie bialgebras Yang-Baxter equation Lie algebra of generalized Witt type |
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