A minimal action of the compact quantum group \(SU_q(n)\) on a full factor. (English) Zbl 0928.46049

Summary: Based on the free product construction we show that a certain full factor of type \(\text{III}_{q^2}\) admits a minimal coaction of the compact quantum group \(\text{SU}_q(n)\). Minimal coactions of compact Kac algebras are also investigated by the same technique.


46L55 Noncommutative dynamical systems
46L35 Classifications of \(C^*\)-algebras
46L40 Automorphisms of selfadjoint operator algebras
46L10 General theory of von Neumann algebras
46L54 Free probability and free operator algebras
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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