Quantum $\mathrm{SO}(3)$ groups and quantum group actions on $M_2$

Abstract

Answering a question of Shuzhou Wang we give a description of quantum SO.3/ groups of Podleś as universal compact quantum groups acting on the C*-algebra M2 and preserving the Powers state. We use this result to give a complete classification of all continuous compact quantum group actions on M2. Mathematics Subject Classification (2010). 46L89, 58B34, 58B32; 17B37, 16W30.