Quantum \(\mathrm{SO}(3)\) groups and quantum group actions on \(M_{2}\). (English) Zbl 1194.46108
Summary: Answering a question of Shuzhou Wang we give a description of quantum \(\mathrm{SO}(3)\) groups of Podleś as universal compact quantum groups acting on the \(C^*\)-algebra \(M_{2}\) and preserving the Powers state. We use this result to give a complete classification of all continuous compact quantum group actions on \(M_{2}\).
MSC:
| 46L89 | Other “noncommutative” mathematics based on \(C^*\)-algebra theory |
| 58B34 | Noncommutative geometry (à la Connes) |
| 58B32 | Geometry of quantum groups |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 16T05 | Hopf algebras and their applications |
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