Topological Hopf algebras, quantum groups and deformation quantization

Philippe Bonneau (1, 2) , Daniel Sternheimer (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 MMAS - Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes

After 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 described

Mots clés: topological vector spaces; quantum groups; deformation quantization; Hopf algebras

Domaines: Algèbres quantiques [math.QA]; Géométrie symplectique [math.SG]; Physique mathématique [math-ph]

Philippe Bonneau, Daniel Sternheimer. Topological Hopf algebras, quantum groups and deformation quantization. 2003. ⟨hal-00000507⟩