$SU_{\mu}(2)$ (where $\mu \in \mathbb{R}^{+}$) is an example of a compact matrix quantum group, as defined by Woronowicz, but is $SU(2) \otimes SU(2) = Spin (4)$ also a compact matrix quantum group?
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1Well, I am not sure, what do you mean by your question. Since it is in particular a compact matrix group, it must then be also a compact matrix quantum group. – Daniel Mar 16 '21 at 16:22