Pierre Bieliavsky

After briefly reviewing certain aspects of the theory of locally compact quantum groups à la Kustermans - Vaes, I will present a simple deformation quantization-based geometrical construction which produces such objects in the context of Fröbenius type groups (in the Lie case, a Lie group is of Fröbenius type if it admits an open coadjoint orbit). I will then show that the theory of symmetric spaces yields smooth analogues of those. I will then comment on their respective behaviour when attending the question of deforming various categories of topological module-algebras. This work is partly joint with Victor Gayral [P.B.,V. Gayral; Mem. AMS 2015] and Victor Gayral, Sergei Neyshveyev and Lars Tuset [P.B.,V. Gayral, S. Neyshveyev, L.Tuset; J. Funct. Analysis 2022 ].