  Let G be a connected, simply connected Poisson-Lie group with quasitriangular
Lie bialgebra g. An explicit description of the double D(g) is given, together
with the embeddings of g and g^*. This description is then used to provide a
construction of the double D(G). The aim of this work is to describe D(G) in
sufficient detail to be able to apply the procedures of Semenov-Tian-Shansky
and Drinfeld for the classification of symplectic leaves and Poisson
homogeneous spaces for Poisson-Lie groups.
