In this talk, we will explain the existence of a universal braided compact quantum group acting on a graph C*-algebra in the twisted monoidal category of C*-algebras equipped with an action of the circle group. Along the way, we shall also present a braided version of the free unitary quantum group (over the circle group), which plays a crucial role in the previous construction. Finally, we will compute the braided compact quantum symmetry group for the Cuntz algebra. This is a joint work with Suvrajit Bhattacharjee and Soumalya Joardar.
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