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A VON NEUMANN ALGEBRA CHARACTERIZATION OF PROPERTY (T) FOR GROUPOIDS

Part of: Groupoids Ergodic theory Selfadjoint operator algebras

Published online by Cambridge University Press:  21 December 2018

MARTINO LUPINI Open the ORCID record for MARTINO LUPINI [Opens in a new window]
MARTINO LUPINI*
Affiliation:
Victoria University of Wellington, School of Mathematics & Statistics, PO Box 600, 6140Wellington, New Zealand email martino.lupini@vuw.ac.nz
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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 inclusions $L(H)\subset L(G)$.

Keywords

groupoidvon Neumann algebraproperty (T)Kazhdan groupoidbimodulecohomologyrepresentation

MSC classification

Primary: 20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms)
Secondary: 46L10: General theory of von Neumann algebras 37A15: General groups of measure-preserving transformations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 363 - 386
Copyright
© 2018 Australian Mathematical Publishing Association Inc.

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Footnotes

The author was partially supported by the NSF Grant DMS-1600186.

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