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.

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

References in corpus (3)

• Quantum Symmetry on Potts Model
• Anyonic quantum symmetries of finite spaces
• Cocycle twisting of semidirect products and transmutation

Cited by in corpus (1)

• Cocycle twisting of semidirect products and transmutation