Answering a question of Shuzhou Wang we give a description of quantum $\SO(3)$ groups of Podle\'s as universal objects. We use this result to give a complete classification of all continuous compact quantum group actions on $M_2$.
On quantum semigroup actions on finite quantum spaces
Quantum spheres as graph and groupoid C*-algebras: a review
Irreducible representations of the crystallisation of the $C^{*}$-algebra $C(SU_{q}(n+1))$
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