Michael Brannan

Approximation properties for free orthogonal and free unitary quantum groups

Abstract In this paper, we study the structure of the reduced C*-algebras and von Neumann algebras associated to the free orthogonal and free unitary quantum groups. We show that the reduced von Neumann algebras of these quantum groups always have the Haagerup approximation property. Combining this result with a Haagerup-type inequality due to Vergnioux, we also show that the reduced C*-algebras always have the metric approximation property.

The Connes embedding property for quantum group von Neumann algebras

For a compact quantum group

Quantum Symmetries and Strong Haagerup Inequalities

\mathbb G

Strong Asymptotic Freeness for Free Orthogonal Quantum Groups

of Kac type, we study the existence of a Haar trace-preserving embedding of the von Neumann algebra

ERROR ESTIMATES FOR DOMINICI’S HERMITE FUNCTION ASYMPTOTIC FORMULA AND SOME APPLICATIONS

L^\infty(\mathbb G)

Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

into an ultrapower of the hyperfinite II

Quantum Groups, Property (T), and Weak Mixing

_1

Orthogonal free quantum group factors are strongly 1-bounded

-factor (the Connes embedding property for

Extending multipliers of the Fourier algebra from a subgroup

L^\infty(\mathbb G)

Quantum groups and generalized circular elements

). We establish a connection between the Connes embedding property for