PreprintarXiv licencearXiv
A groupoid model for Rørdam's finite-infinite C*-algebra
Abstract
We construct a groupoid model for Rordam's example of a simple, nuclear, separable C*-algebra containing a finite and an infinite projection. This groupoid model arises from a (crossed product of a) carefully chosen model for the inductive limit construction in Rordam's original approach, which we show to yield a Cartan subalgebra of the limit. In particular, this procedure yields a locally compact, second countable, Hausdorff, étale, amenable, minimal and topologically principal groupoid whose unit space is compact, and whose C*-algebra contains an infinite and a non-zero finite projection. Hence, this groupoid is amenable, and yet does not have comparison.
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BibTeX
@misc{keuppens2026groupoid,
title = {{A groupoid model for Rørdam's finite-infinite $C^*$-algebra}},
author = {Drieke Keuppens and Diego Martínez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01543},
eprint = {2610.01543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01543},
}
RIS
TY - UNPB
TI - A groupoid model for Rørdam's finite-infinite C^*-algebra
AU - Drieke Keuppens
AU - Diego Martínez
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01543
UR - https://arxiv.org/abs/2610.01543
AB - We construct a groupoid model for Rordam's example of a simple, nuclear, separable C^*-algebra containing a finite and an infinite projection. This groupoid model arises from a (crossed product of a) carefully chosen model for the inductive limit construction in Rordam's original approach, which we show to yield a Cartan subalgebra of the limit. In particular, this procedure yields a locally compact, second countable, Hausdorff, étale, amenable, minimal and topologically principal groupoid whose unit space is compact, and whose C^*-algebra contains an infinite and a non-zero finite projection. Hence, this groupoid is amenable, and yet does not have comparison.
ER -