When amenable groups have real rank zero $C^*$-algebras

Iason Moutzouris

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arXiv · 2306.07231

When amenable groups have real rank zero $C^*$-algebras

Iason Moutzouris

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Abstract

We investigate when discrete, amenable groups have $C^*$-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then all normal subgroups of $G$ that are elementary amenable and have finite Hirsch length must be locally finite.

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Iason Moutzouris. 2023-06-12. When amenable groups have real rank zero $C^*$-algebras. https://arxiv.org/abs/2306.07231

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