
Journal of Lie Theory 25 (2015), No. 3, 775786 Copyright Heldermann Verlag 2015 Lie Bialgebra Structures on NotFinitely 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 [Abstractpdf] Lie bialgebra structures on a class of notfinitely 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 [ Fulltextpdf (292 KB)] for subscribers only. 