Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 25 (2015), No. 3, 775--786Copyright 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 [ Fulltext-pdf  (292  KB)] for subscribers only.