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A von Neumann algebra characterization of property (T) for groupoids (1708.01763v1)

Published 5 Aug 2017 in math.OA and math.DS

Abstract: For an arbitrary discrete probability-measure-preserving groupoid $G$, we provide a characterization of property (T) for $G$ in terms of the groupoid von Neumann algebra $L(G)$. More generally, we obtain a characterization of relative property (T) for a subgroupoid $H\subset G$ in terms of the inclusion $L\left( H\right) \subset L\left( G\right) $.

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