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PreprintCC BY 4.0arXiv

Operator systems in étale groupoid C*-algebras

  • Georgios Baziotis
  • Douglas Farenick
  • Evgenios T. A. Kakariadis
  • Malte Leimbach
  • Lyudmila Turowska
  • Walter D. van Suijlekom
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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.

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Cite

BibTeXRIS
BibTeX
@misc{baziotis2026operator,
  title = {{Operator systems in étale groupoid C*-algebras}},
  author = {Georgios Baziotis and Douglas Farenick and Evgenios T. A. Kakariadis and Malte Leimbach and Lyudmila Turowska and Walter D. van Suijlekom},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34269},
  eprint = {2610.34269},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34269},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Operator systems in étale groupoid C*-algebras
AU  - Georgios Baziotis
AU  - Douglas Farenick
AU  - Evgenios T. A. Kakariadis
AU  - Malte Leimbach
AU  - Lyudmila Turowska
AU  - Walter D. van Suijlekom
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34269
UR  - https://arxiv.org/abs/2610.34269
AB  - 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.
ER  -