Geodesic
The simplex of tracial quantum symmetric states
Yoann Dabrowski 1   ; Kenneth J. Dykema 2   ; Kunal Mukherjee 3
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
Studia Mathematica, Tome 225 (2014) no. 3, pp. 203-218 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm225-3-2
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

Yoann Dabrowski  1   ; Kenneth J. Dykema  2   ; Kunal Mukherjee  3

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 
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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

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