Uniqueness questions for C*-norms on group rings

TL;DR

This paper investigates the conditions under which complex group rings of certain amenable groups admit multiple C*-completions, addressing a question about the uniqueness of C*-norms.

Contribution

It identifies a broad class of amenable groups with non-unique C*-norms on their group rings, providing evidence against the uniqueness conjecture.

Findings

Existence of multiple C*-completions for certain amenable groups

Partial evidence towards non-uniqueness of C*-norms

Addresses a question posed by Grigorchuk, Musat, and R{ extbackslash}ordam

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 R{\o}rdam.