The simplex of tracial quantum symmetric states
Volume 225 / 2014
Studia Mathematica 225 (2014), 203-218
MSC: Primary 46L54; Secondary 46L53.
DOI: 10.4064/sm225-3-2
Abstract
We show that the space of tracial quantum symmetric states of an arbitrary unital $C^*$-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital $C^*$-algebra free product of $A$ with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when $A$ is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product $C^*$-algebras.
