We construct some braided quantum groups over the circle group. These are analogous to the free orthogonal quantum groups. They generalise the braided quantum SU(2) groups for a complex deformation parameter. We describe their irreducible representations and fusion rules and study when they are monoidally equivalent. A key tool here is to describe the bosonisation of our braided compact quantum groups through ordinary free orthogonal quantum groups.

中文翻译：

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编织自由正交量子群

我们在圆组上构造了一些编织量子组。这些类似于自由正交量子基团。他们将编织量子SU（2）基团推广为一个复杂的变形参数。我们描述它们的不可约表示和融合规则，并研究它们的单等价形式。这里的关键工具是通过普通的自由正交量子组描述编织的紧密量子组的玻化。