Tracial states on groupoid C*-algebras and essential freeness

Li K, Zhang J (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Journal of Noncommutative Geometry European Mathematical Society

Book Volume: 20

Pages Range: 561-586

Journal Issue: 2

DOI: 10.4171/JNCG/597

Abstract

Let [Formula presented] be a locally compact Hausdorff étale groupoid. We call a tracial state on a general groupoid C*-algebra [Formula presented] canonical if [Formula presented], where [Formula presented] is the canonical conditional expectation. In this paper, we consider so-called fixed point traces on Cc.[Formula presented], and prove that [Formula presented] is essentially free if and only if any tracial state on [Formula presented] is canonical and any fixed point trace is extendable to [Formula presented] As applications, we obtain the following: (1) a group action is essentially free if every tracial state on the reduced crossed product is canonical and every isotropy group is amenable; (2) if the groupoid [Formula presented] is second-countable, amenable and essentially free then every (not necessarily faithful) tracial state on the reduced groupoid C*-algebra is quasidiagonal.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Fudan University / 复旦大学 CN China (CN)

How to cite

APA:

Li, K., & Zhang, J. (2026). Tracial states on groupoid C*-algebras and essential freeness. Journal of Noncommutative Geometry, 20(2), 561-586. https://doi.org/10.4171/JNCG/597

MLA:

Li, Kang, and Jiawen Zhang. "Tracial states on groupoid C*-algebras and essential freeness." Journal of Noncommutative Geometry 20.2 (2026): 561-586.

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