Embeddings into the ultrapower of the Jiang-Su algebra

TL;DR

This paper investigates the conditions under which cones over separable C*-algebras and certain continuous fields embed into ultrapowers of the Jiang-Su algebra and the Razak-Jacelon algebra, expanding understanding of their embedding properties.

Contribution

It demonstrates that cones over any separable C*-algebra embed into ultrapowers of both $\

Findings

Cones over separable C*-algebras embed into ultrapowers of $\

Generalizes embedding results to continuous fields with well-behaved fibers

Provides new insights into the structure of ultrapowers of $\

Abstract

We study existence of embeddings into ultrapowers of the Jiang-Su algebra $\mathcal{Z}$ and the Razak-Jacelon algebra $\mathcal{W}$. More specifically, we show that the cone over any separable $C^*$-algebra embeds into the ultrapowers of both $\mathcal{Z}$ and $\mathcal{W}$. We also show that the result for $\mathcal{Z}$ generalizes to separable and exact continuous fields of $C^*$-algebras for which one of the fibers embeds into the ultrapower of $\mathcal{Z}$, if this fiber is suitably well-behaved.