Tracial Rokhlin property for actions of amenable groups on C* algebras

TL;DR

This paper extends the concept of the tracial Rokhlin property to actions of amenable groups on simple C*-algebras, broadening its applicability and demonstrating its relevance through natural examples.

Contribution

It provides a further generalization of the tracial Rokhlin property for amenable group actions and shows that many known results extend under this new framework.

Findings

Many known results about the tracial Rokhlin property are generalized to amenable group actions.

Some natural examples exhibit the (weak) tracial Rokhlin property.

The new definition encompasses broader classes of group actions on C*-algebras.

Abstract

Tracial Rokhlin property was introduced by Chris Phillips to study the structure of crossed product of actions on simple C*-algebras. It was originally defined for actions of finite groups and group of integers. Matui and Sato generalized it to actions of amenable groups. In this paper, we give a further generalization of Matui and Sato's definition. We shall show that many known results about tracial Rokhlin property could be generalized to actions of amenable groups under this definition. We also show that some natural examples has the (weak) tracial Rokhlin property.