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

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

https://doi.org/10.1142/S0129167X23500921Cited by:0 (Source: Crossref)

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 is 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.

Communicated by Yasuyuki Kawahigashi

Keywords:

AMSC: 22D25, 46L05

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