The Tracial Rokhlin Property for Compact Group Actions

The Rokhlin property and the tracial Rokhlin property for actions of finite groups are now well known and have been studied systematically. The Rokhlin property for actions of compact groups has also been studied systematically. We define and investigate systematically and in-depth the tracial Rokhlin property for action of second countable compact groups on simple unital C*-algebras. Our property, allows us to prove permanence properties and expected theorems, is an exact generalization of the tracial Rokhlin property for actions of finite groups on classifiable C*-algebras (in the sense of the Elliott program), and admits examples.

This is joint work with N. Christopher Phillips.