Journal of Lie Theory 25 (2015), No. 3, 775--786
Copyright Heldermann Verlag 2015
Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type
Hao Wang
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China
wangh228@mail.ustc.edu.cn
Ying Xu
Dept. of Mathematics, Hefei University of Technology, Hefei 230009 -- Anhui, P. R. China
xuying@hfut.edu.cn
Xiaoqing Yue
Dept. of Mathematics, Tongji University, Shanghai 200092, P. R. China
xiaoqingyue@tongji.edu.cn
[Abstract-pdf]
Lie bialgebra structures on a class of not-finitely graded Lie algebras $B(\Gamma)$ of Block type are investigated. By proving the triviality of the first cohomology group of $B(\Gamma)$ with coefficients in its adjoint tensor module, namely, $H^1(B(\Gamma),B(\Gamma)\otimes B(\Gamma))=0$, we obtain that all Lie bialgebra structures on $B(\Gamma)$ are triangular coboundary.
Keywords: Lie bialgebras, derivation, cohomology group, Lie algebras of Block type.
MSC: 17B10, 17B65, 17B68
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