# Trace scaling automorphisms of the stabilized Razak-Jacelon algebra

## TL;DR

This paper classifies trace scaling automorphisms of a specific simple, nuclear, stably projectionless C*-algebra with trivial K-groups, and explores automorphisms with the Rohlin property, providing new insights into their structure.

## Contribution

It provides a classification of trace scaling automorphisms of the stabilized Razak-Jacelon algebra and shows all automorphisms with the Rohlin property are outer conjugate.

## Key findings

- All trace scaling automorphisms are classified up to outer conjugacy.
- Automorphisms with the Rohlin property are all outer conjugate.
- The central sequence algebra of the Razak-Jacelon algebra is infinite.

## 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$^*$-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$^*$-algebra $F(\mathcal{W})$ of $\mathcal{W}$ is infinitee, which answers a question of Kirchberg.