IUMJ

Title: Characterization of product-type actions with the Rokhlin properties

Authors: Qingyun Wang

Issue: Volume 64 (2015), Issue 1, 295-308

Abstract:

Product-type actions are used to construct explicit examples of Rokhlin actions. It is then interesting to see whether we can give an explicit criterion to determine whether a given product-type action has the Rokhlin properties. Phillips gave a characterization for $\mathbb{Z}/2\mathbb{Z}$-actions in [N. Christopher Phillips, \textit{Finite cyclic group actions with the tracial Rokhlin property} (September, 2006)], and asked whether similar
characterization could be found for a general finite group. In this paper, we answer this affirmatively, and give a simple characterization in terms of the unitary representations defining the product-type action.