When amenable groups have real rank zero C∗-algebras

Iason Moutzouris

Type: Article

Publication Date: 2023-09-30

Citations: 0

DOI: https://doi.org/10.1142/s0129167x23500921

Abstract

We investigate when discrete, amenable groups have [Formula: see text]-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 [Formula: see text] has real rank zero, then all normal subgroups of [Formula: see text] that are elementary amenable and have finite Hirsch length must be locally finite.

Locations

International Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

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+	Introduction to the Baum-Connes Conjecture	2002	Alain Valette
+	Characteristic subgroups in locally finite groups	2011	N. Yu. Makarenko Pavel Shumyatsky
+	C∗-algebras of real rank zero	1991	Lawrence G. Brown Gert K. Pedersen
+	Continuous fields of C*-algebras over finite dimensional spaces	2009	Marius Dădărlat
+	Free subgroups in linear groups	1972	Jacques Tits
+	Reduction of real rank in inductive limits ofC *-algebras	1992	Bruce Blackadar Ola Bratteli George A. Elliott Alexander Kumjian
+ PDF Chat	Group 𝐶*-algebras of real rank zero or one	1993	Eberhard Kaniuth
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+ PDF Chat	Projections in free product C $^*$ -algebras, II	2000	Kenneth J. Dykema Mikael Rørdam
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