2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68133After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities and provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described13 pages, to appear in the proceedings of the conference "Hopf algebras in noncommutative geometry and physics" (VUB, Brussels, May 2002)Quantum AlgebraMathematical PhysicsSymplectic Geometry54C40, 14E20 (primary) 46E25, 20C20 (secondary)text