# The generator problem for Z-stable C*-algebras

@article{Thiel2012TheGP,
title={The generator problem for Z-stable C*-algebras},
author={Hannes Thiel and Wilhelm Winter},
journal={arXiv: Operator Algebras},
year={2012}
}
• Published 18 January 2012
• Mathematics
• arXiv: Operator Algebras
The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebras A is singly generated, which means that there exists an element x in A that is not contained in any proper sub-C*-algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a…
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