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Braided quantum symmetries of graph $\mathrm{C}^*$-algebras (2201.09885v3)
Published 24 Jan 2022 in math.OA and math.QA
Abstract: We prove the existence of a universal braided compact quantum group acting on a graph $\mathrm{C}*$-algebra in the category of $\mathbb{T}$-$\mathrm{C}*$-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.