PreprintarXiv licencearXiv
A characterization of simplicity of reduced groupoid C*-algebras
Abstract
We show that, for a second-countable locally compact Hausdorff étale minimal groupoid with compact unit space, simplicity of the reduced groupoid C*-algebra implies the existence of a comeager set of unit points with C*-simple isotropy group. Combining this result with work of Christensen and Neshveyev on exotic completions of isotropy group algebras, we show that the converse implication is also true. Finally, we construct a Hausdorff étale minimal groupoid with an isotropy group whose induced exotic completion differs from its reduced group C*-algebra, answering a question of Christensen and Neshveyev.
Related
- Von Neumann algebras as reduced twisted groupoid C*-algebras
- Simplicity of reduced crossed products
- Operator systems in étale groupoid C*-algebras
- Pullbacks of Groupoid C*-Algebras over Disjoint Invariant Sets
- Simplicity and pure infiniteness for C*-algebras associated with stabilizers of boundary actions
BibTeX
@misc{boldrini2026characterization,
title = {{A characterization of simplicity of reduced groupoid C*-algebras}},
author = {Paolo Boldrini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21553},
eprint = {2609.21553},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21553},
}
RIS
TY - UNPB
TI - A characterization of simplicity of reduced groupoid C*-algebras
AU - Paolo Boldrini
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21553
UR - https://arxiv.org/abs/2609.21553
AB - We show that, for a second-countable locally compact Hausdorff étale minimal groupoid with compact unit space, simplicity of the reduced groupoid C*-algebra implies the existence of a comeager set of unit points with C*-simple isotropy group. Combining this result with work of Christensen and Neshveyev on exotic completions of isotropy group algebras, we show that the converse implication is also true. Finally, we construct a Hausdorff étale minimal groupoid with an isotropy group whose induced exotic completion differs from its reduced group C*-algebra, answering a question of Christensen and Neshveyev.
ER -