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

Abstract

We prove the existence of a universal braided compact quantum group acting on a graph ${\mathrm{C}}^{\ast }$-algebra in the category of $\mathbb{T}$-${\mathrm{C}}^{\ast }$-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.

arXiv commentRevised version following the referee's suggestions. To appear in International Journal of Mathematics

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Cited by in corpus (2)

• Cocycle twisting of semidirect products and transmutation
• Braided quantum groups and their bosonizations in the $C^{\ast }$-algebraic framework