A groupoid model for Rørdam's finite-infinite $C^*$-algebra

Drieke Keuppens; Diego Martínez

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arXiv · 2610.01543

A groupoid model for Rørdam's finite-infinite $C^*$-algebra

Drieke Keuppens·Diego Martínez

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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 RIS

Drieke Keuppens, Diego Martínez. 2026-10-01. A groupoid model for Rørdam's finite-infinite $C^*$-algebra. https://arxiv.org/abs/2610.01543

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