## Linear Analysis Seminar

**Date: ** December 6, 2019

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

**Location: ** BLOC 220

**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.