Actions of compact quantum groups on operator algebras. (English) Zbl 0960.58004

The author reports (without proofs) his recent results on actions of \(SU_q(2)\) quantum group on operator algebras. The mathematical structure is parallel to the boundary theory of random walks on discrete groups where a discrete group is replaced by the dual Hopf algebra of \(SU_q(2)\) and a random walk by the completely positive noncommutative Markov operator.


58B32 Geometry of quantum groups
46L55 Noncommutative dynamical systems
17B37 Quantum groups (quantized enveloping algebras) and related deformations
46L53 Noncommutative probability and statistics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory