$\mathcal{Z}$ is universal

Abstract

We use order zero maps to express the Jiang–Su algebra $\mathcal{Z}$ as a universal C*-algebra on countably many generators and relations, and we show that a natural deformation of these relations yields the stably projectionless algebra $\mathcal{W}$ studied by Kishimoto, Kumjian and others. Our presentation is entirely explicit and involves only *-polynomial and order relations.