Noncommutative Choquet simplices

Speaker:
Matthew Kennedy, University of Waterloo

Event:
The 48th Canadian Operator Symposium

Title:
Noncommutative Choquet simplices

Recently, Ken Davidson and I introduced a new framework for noncommutative convexity, along with a corresponding noncommutative Choquet theory that generalizes much of classical Choquet theory. In this talk, I will discuss a notion of noncommutative Choquet simplex, which generalizes the classical notion of Choquet simplex and turns out to play an analogous role in noncommutative dynamics. I will discuss some applications, including the following extension of Glasner and Weiss’s characterization of groups with Kazhdan’s property (T): a group has property (T) if and only if whenever it acts on a C*-algebra, the set of invariant states is affinely homeomorphic to the state space of a C*-algebra. This is joint work with Eli Shamovich.

[stellaseremetaki]

NONCOMMUTATIVE CHOQUET SIMPLICESMATTHEW KENNEDY AND ELI SHAMOVICH

Abstract