A von Neumann algebra characterization of property (T) for groupoids
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) $.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.01763
- arXiv:
- arXiv:1708.01763
- Bibcode:
- 2017arXiv170801763L
- Keywords:
-
- Mathematics - Operator Algebras;
- Mathematics - Dynamical Systems;
- 20L05;
- 46L10 (Primary) 37A15 (Secondary)
- E-Print:
- J. Aust. Math. Soc. 108 (2020) 363-386