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

Izumi, Masaki

RIMS Kokyuroku 1024, 55-60 (1998).

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.

Reviewer: Robert Alicki (Gdansk)

MSC:

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

Keywords:

quantum groups; Hopf algebras; noncommutative Markov operators