Braided Free Orthogonal Quantum Groups

Abstract 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.