Geodesic
The simplex of tracial quantum symmetric states
Yoann Dabrowski1 ; Kenneth J. Dykema2 ; Kunal Mukherjee3
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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