Z is universal

TL;DR

This paper presents an explicit universal C*-algebra presentation of the Jiang-Su algebra Z using order zero maps, and introduces a deformation leading to the stably projectionless algebra W, connecting these structures explicitly.

Contribution

It provides a new explicit presentation of Z and a deformation that produces W, linking these important C*-algebras through generators and relations.

Findings

Z is expressed as a universal C*-algebra with generators and relations.

A deformation of relations yields the algebra W.

The presentation involves only *-polynomial and order relations.

Abstract

We use order zero maps to express the Jiang-Su algebra 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 W studied by Kishimoto, Kumjian and others. Our presentation is entirely explicit and involves only *-polynomial and order relations.