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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

Ying Xu
Dept. of Mathematics, Hefei University of Technology, Hefei 230009 -- Anhui, P. R. China

Xiaoqing Yue
Dept. of Mathematics, Tongji University, Shanghai 200092, P. R. China


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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