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

TL;DR

This paper characterizes quantum SO(3) groups as universal objects and classifies all continuous compact quantum group actions on the 2x2 matrix algebra M_2, advancing understanding of quantum symmetries.

Contribution

It provides a universal description of quantum SO(3) groups and a complete classification of their actions on M_2, answering a question posed by Shuzhou Wang.

Findings

Quantum SO(3) groups are described as universal objects.

Complete classification of quantum group actions on M_2.

Advances understanding of quantum symmetries on matrix algebras.

Abstract

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 $M_2$.