Noncommutative Choquet simplices

  title={Noncommutative Choquet simplices},
  author={Matthew Kennedy and Eli Shamovich},
  journal={Mathematische Annalen},
  pages={1591 - 1629}
We introduce a notion of noncommutative Choquet simplex, or briefly an nc simplex, that generalizes the classical notion of a simplex. While every simplex is an nc simplex, there are many more nc simplices. They arise naturally from C*-algebras and in noncommutative dynamics. We characterize nc simplices in terms of their geometry and in terms of structural properties of their corresponding operator systems. There is a natural definition of nc Bauer simplex that generalizes the classical… 

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