Trace scaling automorphisms of the stabilized Razak-Jacelon algebra

Abstract

We classify trace scaling automorphisms of $\mathcal{W}\otimes \mathbb{K}$ up to outer conjugacy, where $\mathcal{W}$ is a certain simple separable nuclear stably projectionless C${}^{\ast }$-algebra having trivial $K$-groups. Also, we show that all automorphisms of $\mathcal{W}$ with the Rohlin property are outer conjugate to each other. Moreover, we show that the central sequence C${}^{\ast }$-algebra $F(\mathcal{W})$ of $\mathcal{W}$ is infinitee, which answers a question of Kirchberg.

30 pages. v3:Title changed. v2:We added Theorem 5.8, Corollary 5.9(an answer to Kirchberg's question), Question 5.10 and Corollary 5.11

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• A characterization of the Razak-Jacelon algebra
• Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra
• Rohlin actions of finite groups on the Razak-Jacelon algebra