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Compact quantum ergodic systems. (English) Zbl 1137.46041

Summary: We develop the theory of multiplicity maps for compact quantum groups. As an application, we obtain a complete classification of right coideal \(C^{*}\)-algebras of \(C(SU_q(2))\) for \(q\in [ - 1,1) \backslash \{0\}\). They are labeled with Dynkin diagrams, but the classification results for positive and negative cases of \(q\) are different. Many of the coideals are quantum spheres or quotient spaces by quantum subgroups, but we also have other ones in our classification list.

MSC:

46L65 Quantizations, deformations for selfadjoint operator algebras
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
58B32 Geometry of quantum groups
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