Vol. 298, No. 2, 2019

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Uniqueness questions for $C^*$-norms on group rings

Vadim Alekseev and David Kyed

Vol. 298 (2019), No. 2, 257–266
Abstract

We provide a large class of discrete amenable groups for which the complex group ring has several C*-completions, thus providing partial evidence towards a positive answer to a question raised by Rostislav Grigorchuk, Magdalena Musat and Mikael Rørdam.

Keywords
group rings, C*-norms, the Atiyah conjecture
Mathematical Subject Classification 2010
Primary: 16S34, 46L05, 46L10
Milestones
Received: 17 August 2018
Accepted: 27 August 2018
Published: 8 March 2019
Authors
Vadim Alekseev
Institut für Geometrie
Fakultät Mathematik
Technische Universität Dresden
Dresden
Germany
David Kyed
Department of Mathematics and Computer Science
University of Southern Denmark
Odense
Denmark