Michael Brannan, Texas A M University
“Matricial microstates for quantum group von Neumann algebras”
An important conjecture in the theory of operator algebras, commonly referred to as the “Connes Embedding Conjecture”, states that for any finite von Neumann algebra M and any n- tuple (x1 , ...., xn ) of self-adjoint generators of M , there exist sequences of finite dimensional self- adjoint matrices which asymptotically model the n-tuple (x1, ..., xn) in a suitable distributional sense. Such families of matrix approximants are called “matricial microstates” for the n-tuple (x1, ..., xn).
In this talk I will describe a representation theoretic approach to building matricial mi- crostates for generators of von Neumann algebras associated to compact quantum groups. Using this approach we prove that the II1 factors associated to free orthogonal quantum groups are Connes embeddable. Time permitting, we will also discuss some applications to free entropy dimension calculations and QWEP for the associated reduced C∗-algebras.
(This is joint work with Benoit Collins and Roland Vergnioux).
**Please Note Special Date and Room**