1Université de Lyon Université Lyon 1 Institut Camille Jordan UMR 5208 43 blvd. du 11 novembre 1918 F-69622 Villeurbanne Cedex, France 2Department of Mathematics Texas A&M University College Station, TX 77843-3368, U.S.A. 3Department of Mathematics Indian Institute of Technology Madras Chennai 600 036, India
Studia Mathematica, Tome 225 (2014) no. 3, pp. 203-218
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.
Keywords:
space tracial quantum symmetric states arbitrary unital * algebra choquet simplex face tracial state space universal unital * algebra product itself infinitely many times extreme points simplex dense making poulsen simplex separable nontrivial course proof characterize centers certain tracial amalgamated product * algebras
1
Université de Lyon Université Lyon 1 Institut Camille Jordan UMR 5208 43 blvd. du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
2
Department of Mathematics Texas A&M University College Station, TX 77843-3368, U.S.A.
3
Department of Mathematics Indian Institute of Technology Madras Chennai 600 036, India
@article{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},
pages = {203--218},
year = {2014},
volume = {225},
number = {3},
doi = {10.4064/sm225-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm225-3-2/}
}
TY - JOUR
AU - Yoann Dabrowski
AU - Kenneth J. Dykema
AU - Kunal Mukherjee
TI - The simplex of tracial quantum symmetric states
JO - Studia Mathematica
PY - 2014
SP - 203
EP - 218
VL - 225
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm225-3-2/
DO - 10.4064/sm225-3-2
LA - en
ID - 10_4064_sm225_3_2
ER -
%0 Journal Article
%A Yoann Dabrowski
%A Kenneth J. Dykema
%A Kunal Mukherjee
%T The simplex of tracial quantum symmetric states
%J Studia Mathematica
%D 2014
%P 203-218
%V 225
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm225-3-2/
%R 10.4064/sm225-3-2
%G en
%F 10_4064_sm225_3_2
Yoann Dabrowski; Kenneth J. Dykema; Kunal Mukherjee. The simplex of tracial quantum symmetric states. Studia Mathematica, Tome 225 (2014) no. 3, pp. 203-218. doi: 10.4064/sm225-3-2
