Work

The Global Glimm Property for C * ‐algebras of topological dimension zero

Year: 2026

Type: article

Abstract: We show that a ‐algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is nowhere scattered (no hereditary subalgebra admits a finite‐dimensional representation). This solves the Global Glimm Problem in this setting. It follows that nowhere scattered ‐algebras with finite nuclear dimension and topological dimension zero are pure.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70343

Authors: Ping Wong Ng, Hannes Thiel, Eduard Vilalta

Institutions: University of Louisiana at Lafayette, Chalmers University of Technology, University of Gothenburg, Universitat Politècnica de Catalunya

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Generalitat de Catalunya, Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet, Agencia Estatal de Investigación