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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-2,
author = {Yoann Dabrowski and Kenneth J. Dykema and Kunal Mukherjee},
title = {The simplex of tracial quantum symmetric states},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {203-218},
zbl = {1325.46065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-2}
}
Yoann Dabrowski; Kenneth J. Dykema; Kunal Mukherjee. The simplex of tracial quantum symmetric states. Studia Mathematica, Tome 223 (2014) pp. 203-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-2/