Journal of Operator Theory

Volume 95, Issue 1, Winter 2026 pp. 21-49.

Factoriality of groupoid von Neumann algebras

Authors: Tey Berendschot (1), Soham Chakraborty (2), Milan Donvil (3), Se-Jin Kim (4)
Author institution: (1) Department of Mathematics, KU Leuven, Leuven, 3000, Belgium
(2) Department of Mathematics, KU Leuven, Leuven, 3000, Belgium
(3) Department of Mathematics, KU Leuven, Leuven, 3000, Belgium
(4) Department of Mathematics, KU Leuven, Leuven, 3000, Belgium

Summary: We give a characterisation of the factoriality of the groupoid\break von Neumann algebra $L(\mathcal{G})$ associated to a discrete measured groupoid $(\mathcal{G}, \mu)$. We introduce the notion of groupoids with ``infinite conjugacy classes'' and show that this property together with ergodicity of the groupoid is equivalent with factoriality of $L(\mathcal{G})$.

DOI: http://dx.doi.org/10.7900/jot.2024feb29.2472
Keywords: groupoids, von Neumann algebras, factoriality

Contents Full-Text PDF