## Banach and Metric Space Geometry Seminar

**Date: ** December 6, 2019

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 628

**Speaker: **Chris Phillips, University of Oregon

**Title: ***The Cuntz semigroup of the crossed product by a finite group action with the weak tracial Rokhlin property*

**Abstract: **Let A be a simple unital C*-algebra. Suppose that a finite group
G acts on A, and that the action has the weak tracial Rokhlin
property, a generalization of the Rokhlin property which uses
positive elements instead of projections, and is fairly common. We
prove that, after discarding the classes of the nonzero projections,
the Cuntz semigroup of the fixed point algebra is just the fixed
points in the Cuntz semigroup of A. For context, for algebras
without strict comparison, the Cuntz semigroup is often very hard
to compute.
As a corollary, we prove that the radius of comparison of the
crossed product satisfies
rc (C^* (G, A)) \leq [1 / card (G)] rc (A).
We also give an example of a simple separable unital AH algebra A
and an action of the two element group G on A which has the Rokhlin
property, and such that rc (A) and rc (C^* (G, A)) are both strictly
positive.
The way the weak tracial Rokhlin property is used in the proof is
different from the usual methods in C*-algebras.
Joint work with M. Ali Asadi-Vasfi and Nasser Golestani.