Stably projectionless Fra\"iss\'e limits

TL;DR

This paper constructs certain C*-algebras, including $ ext{W}$ and $ ext{Z}_0$, as Fra"issé limits of specific classes of structures, demonstrating their generic nature without relying on classification theorems.

Contribution

It provides a new Fra"issé-theoretic framework for realizing stably projectionless C*-algebras, expanding the understanding of their generic properties.

Findings

Realization of algebra $ ext{W}$ as a Fra"issé limit.

Construction of algebra $ ext{Z}_0$ as a Fra"issé limit.

Identification of $ ext{Z}_0 igotimes A$ with $A$ a UHF algebra.

Abstract

We realise the algebra $\mathcal W$, the algebra $\mathcal Z_0$ and the algebras $\mathcal Z_0\otimes A$, where $A$ is a unital UHF algebra as Fra\"iss\'e limits of suitable classes of structures. In doing so, we show that such algebras are generic objects without the use of any classification result.