Lie Bialgebras of Generalized WITT Type,II |
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| Authors: | Yuezhu Wu Guang'ai Song Yucai Su |
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| Affiliation: | 1. Department of Mathematics , Shanghai Jiao Tong University , Shanghai, China;2. Department of Mathematics , Qufu Normal University , Qufu, China yuezhu@maths.usyd.edu.au;4. College of Mathematics and Information Science, Shandong Institute of Business and Technology , Yantai, China;5. Department of Mathematics , University of Science and Technology of China , Hefei, China |
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| Abstract: | In an article by Michaelis, a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In a recent article by Song and Su, Lie bialgebra structures on graded Lie algebras of generalized Witt type with finite dimensional homogeneous components were considered. In this article we consider Lie bialgebra structures on the graded Lie algebras of generalized Witt type with infinite dimensional homogeneous components. By proving that the first cohomology group H1(𝒲, 𝒲 ? 𝒲) is trivial for any graded Lie algebras 𝒲 of generalized Witt type with infinite dimensional homogeneous components, we obtain that all such Lie bialgebras are triangular coboundary. |
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| Keywords: | Lie algebras of generalized Witt type Lie bialgebras Yang-Baxter equation |
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