Abstract
We construct a family of $q$-deformations of SU(2) for complex parameters $q \neq 1$. For real $q$, the deformation coincides with the compact quantum SU$\_q$(2) group. For $q \notin \mathbb R$, SU$\_q$(2) is only a braided compact quantum group with respect to a twisted tensor product functor for C\*-algebras with an action of the circle group.
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