Finite group actions on certain stably projectionless C*-algebras with the Rohlin property

TL;DR

This paper studies finite group actions with the Rohlin property on stably projectionless C*-algebras, providing new examples, properties, and classification results, especially on the Razak-Jacelon algebra, advancing understanding of symmetries in these algebras.

Contribution

It introduces the Rohlin property and approximate representability for such actions, and classifies these actions on specific stably projectionless C*-algebras, extending prior work.

Findings

Defined Rohlin property and approximate representability for these actions

Constructed examples on the Razak-Jacelon algebra

Established classification results for these actions

Abstract

We introduce the Rohlin property and the approximate representability for finite group actions on stably projectionless C*-algebras and study their basic properties. We give some examples of finite group actions on the Razak-Jacelon algebra and show some classification results of these actions. This study is based on the work of Izumi, Robert's classification theorem and Kirchberg's central sequence C*-algebras.