2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77968Let $G$ be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous $G$-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous $G$-spaces and Lagrangian subalgebras in the double $D(g)$ (here $g = Lie G$). A geometric interpretation of some of Poisson homogeneous $G$-spaces is also proposed.LaTeX 2e, 9 pages, to be published in Banach Center Publications; minor changes (typos corrected)Quantum AlgebraDifferential Geometry53C30 (Primary); 17B20, 17B37, 16W30 (Secondary)text