The simplex of tracial quantum symmetric states

Tom 225 / 2014

Yoann Dabrowski, Kenneth J. Dykema, Kunal Mukherjee Studia Mathematica 225 (2014), 203-218 MSC: Primary 46L54; Secondary 46L53. DOI: 10.4064/sm225-3-2


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.


  • Yoann DabrowskiUniversité de Lyon
    Université Lyon 1
    Institut Camille Jordan UMR 5208
    43 blvd. du 11 novembre 1918
    F-69622 Villeurbanne Cedex, France
  • Kenneth J. DykemaDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843-3368, U.S.A.
  • Kunal MukherjeeDepartment of Mathematics
    Indian Institute of Technology Madras
    Chennai 600 036, India

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