Journal of Lie Theory

no. 3
Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 775-786
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.
DOI: 10.5802/jolt.859
Classification: 17B10, 17B65, 17B68
Keywords: Lie bialgebras, derivation, cohomology group, Lie algebras of Block type 
@article{JOLT_2015_25_3_a6,
     author = {H. Wang and Y. Xu and X. Yue},
     title = {Lie {Bialgebra} {Structures} on {Not-Finitely} {Graded} {Lie} {Algebras} {B(\ensuremath{\Gamma})} of {Block} {Type}},
     journal = {Journal of Lie Theory},
     pages = {775--786},
     year = {2015},
     volume = {25},
     number = {3},
     doi = {10.5802/jolt.859},
     zbl = {1359.17033},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.859/}
}
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%A Y. Xu
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H. Wang; Y. Xu; X. Yue. Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 775-786. doi: 10.5802/jolt.859

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