The Global Glimm Property for <i>C</i> <sup>*</sup> ‐algebras of topological dimension zero
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.
Authors
- Hannes Thiel (ORCID: https://orcid.org/0000-0003-0388-6495)
- Ping Wong Ng
- Eduard Vilalta (ORCID: https://orcid.org/0000-0002-1980-9323)
Institutions
- Chalmers University of Technology (SE)
- University of Louisiana at Lafayette (US)
- University of Gothenburg (SE)
- Universitat Politècnica de Catalunya (ES)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-04-01
- DOI
- https://doi.org/10.1112/blms.70343
- Primary Topic
- Advanced Operator Algebra Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Knut och Alice Wallenbergs Stiftelse
- Vetenskapsrådet
- Agencia Estatal de Investigación