Conditional expectations on compact quantum groups and new examples of quantum hypergroups (Q2784967)

A compact quantum hypergroup is a unital \(C^*\)-algebra equipped with a coassociative completely positive coproduct preserving the unit element and satisfying some additional axioms [\textit{Yu. A. Chapovsky} and \textit{L. I. Vainerman}, J. Oper. Theory 41, 261--289 (1999; Zbl 0987.81039)]. The author gives a general construction of compact quantum hypergroups using conditional expectations on compact quantum groups. That enables him to carry out a Delsart-type construction (well-known for the group case) and build several series of non-trivial finite-dimensional quantum hypergroups associated with Kac algebras obtained by twisting the classical series of finite groups.