$\mathcal{Z}$ is universal

Abstract

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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.