Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Keuppens, Drieke, Martínez, Diego
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Fonds Wetenschappelijk Onderzoek
OpenAlex ID: W7215854032