Linearization of Poisson–Lie Structures on the 2d Euclidean and (1 + 1) Poincaré Groups

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.