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

Abstract

Let $A$ and $B$ be simple separable nuclear monotracial C${}^{\ast }$-algebras, and let $\alpha$ and $\beta$ be strongly outer actions of a countable discrete amenable group $\Gamma$ on $A$ and $B$, respectively. In this paper, we show that $\alpha \otimes {\mathrm{id}}_{\mathcal{W}}$ on $A\otimes \mathcal{W}$ and $\beta \otimes {\mathrm{id}}_{\mathcal{W}}$ on $B\otimes \mathcal{W}$ are cocycle conjugate where $\mathcal{W}$ is the Razak-Jacelon algebra. Also, we characterize such actions by using the fixed point subalgebras of Kirchberg's central sequence C${}^{\ast }$-algebras.

some corrections in the proof of Theorem 8.1, generalized some results in Section 4(v3); some corrections; This is an equivariant generalization of arXiv:2008.10235; 32 pages to appear in J. Funct. Anal.

References in corpus (3)

• On classification of non-unital simple amenable C*-algebras, I
• Strongly outer actions of amenable groups on $\mathcal{Z}$-stable nuclear $C^{\ast }$-algebras
• Extensions of C*-algebas by a small ideal