Braided quantum symmetries of graph $\mathrm{C}^*$-algebras

Abstract

We prove the existence of a universal braided compact quantum group acting on a graph C * -algebra in the category of T-C * -algebras with a twisted monoidal structure, in the spirit of the seminal work of S. Wang. To achieve this, we construct a braided analogue of the free unitary quantum group and study its bosonization. As a concrete example, we compute this universal braided compact quantum group for the Cuntz algebra.