Geodesic
Quasi-triangular Hom-Lie Bialgebras
Yuanyuan Chen1 ; Zhongwei Wang1 ; Liangyun Zhang1
1College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China
Journal of Lie Theory, Tome 22 (2012) no. 4, pp. 1075-1089

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

Recently certain twisted Lie algebras, so-called Hom-Lie algebras, and their duals have been considered in the literature. In this paper we investigate boundary and quasi-triangular Hom-Lie bialgebras further. In particular, we characterize the quasi-triangularity of boundary Hom-Lie bialgebras in terms of both a certain Hom-Lie algebra morphism and a certain Hom-Lie coalgebra morphism. We also give a necessary and sufficient condition for a given Hom-Lie algebra and a given 2-tensor to admit a coboundary Hom-Lie bialgebra structure. Finally, we generalize the Drinfeld double of a Lie bialgebra to Hom-Lie bialgebras and discuss the dual codouble.
Classification : 16W30, 17B99, 17B37
Mots-clés : Hom-Lie algebra, Hom-Lie bialgebra, quasi-triangular Hom-Lie bialgebra, (co)double Hom-Lie bialgebra

Yuanyuan Chen  1   ; Zhongwei Wang  1   ; Liangyun Zhang  1

1 College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China 
Yuanyuan Chen; Zhongwei Wang; Liangyun Zhang. Quasi-triangular Hom-Lie Bialgebras. Journal of Lie Theory, Tome 22 (2012) no. 4, pp. 1075-1089. http://geodesic.mathdoc.fr/item/JOLT_2012_22_4_a7/
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     title = {Quasi-triangular {Hom-Lie} {Bialgebras}},
     journal = {Journal of Lie Theory},
     pages = {1075--1089},
     year = {2012},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_4_a7/}
}
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