Generators in $\mathcal{Z}$-stable C*-algebras of real rank zero

TL;DR

This paper proves that in certain well-behaved C*-algebras, a dense set of elements can generate the entire algebra, highlighting the generic nature of generators in these classes.

Contribution

It establishes that all separable, real rank zero, Jiang-Su stable C*-algebras have a dense set of generators, showing generics in classifiable simple nuclear C*-algebras.

Findings

Dense set of generators in Z-stable real rank zero C*-algebras

Generic element is a generator in classifiable simple nuclear C*-algebras

Extension of generator properties to a broad class of C*-algebras

Abstract

We show that every separable C*-algebra of real rank zero that tensorially absorbs the Jiang-Su algebra contains a dense set of generators. It follows that in every classifiable, simple, nuclear C*-algebra, a generic element is a generator.