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arXiv · 1201.3879

The generator problem for Z-stable C*-algebras

Hannes Thiel·Wilhelm Winter
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Abstract

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 discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, the tensor product of two reduced free group C*-algebras is singly generated.

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Hannes Thiel, Wilhelm Winter. 2012-01-18. The generator problem for Z-stable C*-algebras. https://doi.org/10.1090/s0002-9947-2014-06013-3

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