2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59714Let 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.LaTeX2e, 14 pages. Revised version contains new Section 6Quantum Algebra17B62text