$SU(2) \otimes SU(2)$ and Compact Matrix Quantum Groups

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$SU_{\mu}(2)$ (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?