LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS

Bousselham Ganbouri     (Mohammed First University, Mohammed V Avenue, P.O. Box 524, 60000 Oujda, Morocco)
Mohamed Wadia Mansouri     (Ibn Tofail University, P.O. Box 242, 14000 Kénitra, Morocco)

Abstract


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


Poisson-Lie groups, Lie bialgebras, Linearization.

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References


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DOI: http://dx.doi.org/10.15826/umj.2021.2.002

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