Geodesic
Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type
Hao Wang1 ; Ying Xu2 ; Xiaoqing Yue3
1School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China
2Dept. of Mathematics, Hefei University of Technology, Hefei 230009 -- Anhui, P. R. China
3Dept. of Mathematics, Tongji University, Shanghai 200092, P. R. China
Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 775-786

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B10, 17B65, 17B68
Mots-clés : Lie bialgebras, derivation, cohomology group, Lie algebras of Block type

Hao Wang  1   ; Ying Xu  2   ; Xiaoqing Yue  3

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China
2 Dept. of Mathematics, Hefei University of Technology, Hefei 230009 -- Anhui, P. R. China
3 Dept. of Mathematics, Tongji University, Shanghai 200092, P. R. China 
Hao Wang; Ying Xu; Xiaoqing Yue. Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type. Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 775-786. http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a6/
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     author = {Hao Wang and Ying Xu and Xiaoqing 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a6/}
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