The double and dual of a quasitriangular Lie bialgebra

Let G be a connected, simply connected Poisson-Lie group with quasitriangul ar Lie bialgebra g. An explicit description of the double D(g) is given, to gether with the embeddings of g and g*. This description is then used to pr ovide a construction of the double D(G). The aim of this work is to describ e D(G) in sufficient detail to be able to apply the procedures of Semenov-T ian-Shansky and Drinfeld for the classification of symplectic leaves and Po isson homogeneous spaces for Poisson-Lie groups.