Razak–Jacelon代数的非周期自同构

Rohlin actions of finite groups on the Razak-Jacelon algebra

Let $A$ be a simple separable nuclear C$^*$-algebra with a unique tracial state and no unbounded traces, and let $α$ be a strongly outer action of a finite group $G$ on $A$. In this paper, we show that $α\otimes \mathrm{id}$ 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.

有限群在Razak-Jacelon代数上的$\mathcal{W}$-吸收作用

$\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra

本文提出了C$^*$-代数上$\mathcal{W}$-吸收作用的定义，并在共轭与余环共轭意义下完全分类了有限群在Razak-Jacelon代数上的外部$\mathcal{W}$-吸收作用。

Trace scaling automorphisms of the stabilized Razak-Jacelon algebra

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.

Approaching the UCT problem via crossed products of the Razak-Jacelon algebra

We show that the UCT problem for separable, nuclear $\mathrm C^*$-algebras relies only on whether the UCT holds for crossed products of certain finite cyclic group actions on the Razak-Jacelon algebra. This observation is analogous to and in fact recovers a characterization of the UCT problem in terms of finite group actions on the Cuntz algebra $\mathcal O_2$ established in previous work by the authors. Although based on a similar approach, the new conceptual ingredients in the finite context are the recent advances in the classification of stably projectionless $\mathrm C^*$-algebras, as wel…

Razak-Jacelon代数的等变Kirchberg-Phillips型吸收

Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra

本文证明简单可分核单调迹C*-代数上的强外顺从群作用在张量Razak-Jacelon代数后具有余循环共轭的唯一性，并用中心序列代数的不动点子代数给出刻画。

某些无挠顺从群在Razak-Jacelon代数上的强外作用

Strongly outer actions of certain torsion-free amenable groups on the Razak-Jacelon algebra

本文证明了对于特定无挠顺从群类$\mathfrak{C}$中的群$Γ$，其在Razak-Jacelon代数$\mathcal{W}$上的所有强外作用均彼此上闭链共轭，这是Szabó关于强自吸收C$^*$-代数结果的类似结论。