Year: 2026
Type: preprint
Abstract: We study operator systems arising from positivity domains of étale groupoids with compact unit space. Extending Kavruk's enough unitaries principle we show that such operator systems are hyperrigid in the C$^*$-algebra they generate. We focus on operator systems of positivity domains in UHF algebras and, by identifying them with Cantor graph operator systems, we show that they are hyperrigid. Furthermore, we show that in general, such a characterization is not possible when the étaleness condition of the underlying groupoid is removed, due to the failure of reduced spectral and compact operator synthesis.
Source: arXiv (Cornell University)
Institution: Radboud University Nijmegen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, European Commission, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, National Research Foundation of Korea, Vetenskapsrådet, Hellenic Foundation for Research and Innovation, Ministry of Science and ICT, South Korea, Natural Sciences and Engineering Research Council of Canada, NextGenerationEU
Awards: Institut Mittag-Leffler, G3633935216, Noncommutative Analysis in the Theory of Nonlocal Games, Non-commutative analysis for quantum computing, G4286615259, Scale-dependent approach to noncommutative geometry: applications to quantum physics, G6390571125, G754601064, G8626444996, G8680894210, CIF: Small: Fundamental limits in ambiguous communication
OpenAlex ID: W7223890160