Noncommutative Choquet simplices

We introduce a notion of noncommutative Choquet simplex, or briefly an nc that generalizes the classical simplex. While every simplex is there are many more simplices. They arise naturally from C*-algebras and in dynamics. characterize simplices terms their geometry structural properties corresponding operator systems. There natural definition Bauer show compact convex set if only it affinely homeomorphic to state space unital C*-algebra, generalizing result for commutative C*-algebras. obtain several applications states C*-algebra invariant with respect action discrete group From this, we ergodic decomposition theorem uniqueness. Finally, establish new characterization groups Kazhdan’s property (T) extends Glasner Weiss. Specifically, has on C*-algebra.