Geodesic
Linearization of Poisson--Lie structures on the $2D$ Euclidean and $(1+1)$ Poincar\'{e} groups
Ural mathematical journal, Tome 7 (2021) no. 2, pp. 33-42

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The paper deals with linearization problem of Poisson-Lie structures on the $(1+1)$ Poincaré and $2D$ Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine.
Keywords: linearization.
Mots-clés : Poisson-Lie groups, Lie bialgebras 
@article{UMJ_2021_7_2_a1,
     author = {Bousselham Ganbouri and Mohamed Wadia Mansouri},
     title = {Linearization of  {Poisson--Lie} structures on the $2D$ {Euclidean} and $(1+1)$ {Poincar\'{e}}  groups},
     journal = {Ural mathematical journal},
     pages = {33--42},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a1/}
}
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Bousselham Ganbouri; Mohamed Wadia Mansouri. Linearization of  Poisson--Lie structures on the $2D$ Euclidean and $(1+1)$ Poincar\'{e}  groups. Ural mathematical journal, Tome 7 (2021) no. 2, pp. 33-42. http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a1/