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Hamiltonian type Lie bialgebras

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science china mathematics 2007年第9期50卷 1267-1279页

作者： Bin XIN~(1+) guang-ai song~2 Yu-cai su~3 1 Department of mathematics,Shanghai Jiao Tong University,Shanghai 200240,china 2 college of mathematics and information science,shandong institute of business and technology,yantai 264005,china 3 Department of mathematics,University of science and technology of china,Hefei 230026,china Department of mathematics Shanghai Jiao Tong University Shanghai China college of mathematics and information science Shandong Institute of Business and Technology Yantai China Department of mathematics University of Science and Technology of China Hefei China

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H^1(H,H(?)H) is *** then show that all Lie bialgebra structures on H are triangular.

关键词： Lie bialgebra Yang-Baxter equation Hamiltonian Lie algebra 17B62 17B05 17B37 17B66

Dual Lie bialgebra structures of Poisson types

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science china mathematics 2015年第6期58卷 1151-1162页

作者： song guang'ai su yucai college of mathematics and information science Shandong Institute of Business and Technology Department of mathematics Tongji University

Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.

关键词： algebra Poisson commutative maximal associative infinite triangular polynomial multiplication subspace

Lie Bialgebras of Generalized Virasoro-like Type

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1915-1922页

作者： Yue Zhu WU guang ai song Yu Cai su Department of mathematics Shanghai Jiao Tong University Shanghai 200240 P. R. China Department of mathematics Qufu Normal University Qufu 273165 P. R. China college of mathematics and information science Shandong Institute of Business and Technology Yantai 264005 P. R. China Department of mathematics University of Science and Technology of China Hefei 230026 P. R. China

In this paper, Lie bialgebra structures on generalized Virasoro-like algebras are studied. It is proved that all such Lie bialgebras are triangular coboundary.

关键词： Lie bialgebras Yang Baxter equation generalized Virasoro-like algebras