Work

Nonamenable groups whose reduced group C*-algebras are not pure

Year: 2026

Type: preprint

Abstract: We exhibit nonamenable groups whose reduced group C*-algebras are not pure. More precisely, if $Γ$ is any countably infinite discrete group, then the reduced group C*-algebra of the restricted wreath product $(\mathbb{Z}/2\mathbb{Z}) \wr Γ$ has an ideal-quotient isomorphic to $\mathcal{K}(\ell^2(Γ))$. It therefore fails to be nowhere scattered and, in particular, is not pure. Taking $Γ$ to be any nonamenable group, we thereby obtain a negative answer to a question of Thiel.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.10653

Author: Bell, Jamie

Institution: University of Münster

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Chalmers Tekniska Högskola, Göteborgs Universitet

Awards: G1399780489, G1652504919, SFB 1442: Geometrie: Deformationen und Rigidität, EXC 2044: Mathematik Münster: Dynamik – Geometrie – Struktur

OpenAlex ID: W7212311465

Cites: 2

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Related to: 10