Journal of Noncommutative Geometry


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Volume 8, Issue 4, 2014, pp. 1023–1042
DOI: 10.4171/JNCG/176

Published online: 2015-02-02

$\mathcal{Z}$ is universal

Bhishan Jacelon[1] and Wilhelm Winter[2]

(1) Universität Münster, Germany
(2) Westfälische Wilhelms-Universität Münster, Germany

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.

Keywords: Jiang–Su algebra, strongly self-absorbing C*-algebra, stably projectionless C*-algebra, order zero map, classification

Jacelon Bhishan, Winter Wilhelm: $\mathcal{Z}$ is universal. J. Noncommut. Geom. 8 (2014), 1023-1042. doi: 10.4171/JNCG/176