Rohlin actions of finite groups on the Razak-Jacelon algebra

Abstract

Let $A$ be a simple separable nuclear C${}^{\ast }$-algebra with a unique tracial state and no unbounded traces, and let $\alpha$ be a strongly outer action of a finite group $G$ on $A$. In this paper, we show that $\alpha \otimes \mathrm{id}$ on $A\otimes \mathcal{W}$ has the Rohlin property, where $\mathcal{W}$ is the Razak-Jacelon algebra. Combing this result with the recent classification results and our previous result, we see that such actions are unique up to conjugacy.

19 pages. v2:we added references. arXiv admin note: text overlap with arXiv:1704.02414

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