Journal of Operator Theory

Volume 79, Issue 1, Winter 2018 pp. 101-137.

Crossed-products by locally compact groups: Intermediate subfactors

Authors: Remi Boutonnet (1) and Arnaud Brothier (2)
Author institution: (1) Institut de Mathematiques de Bordeaux, Universite de Bordeaux, 351 cours de la Liberation, 33 405 Talence Cedex, France
(2) Department of Mathematics, University of Rome Tor Vergata, Via della Ricerca Scientifica 00133 Roma, Italy

Summary: We study actions of locally compact groups on von Neumann factors and the associated crossed-product von Neumann algebras. In the setting of totally disconnected groups we provide sufficient conditions on an action $G \curvearrowright Q$ ensuring that the inclusion $Q \subset Q \rtimes G$ is irreducible and that every intermediate subfactor is of the form $Q \rtimes H$ for a closed subgroup $H\lhd G$. This partially generalizes previous results obtained by Izumi--Longo--Popa and Choda. We moreover show that one can not hope to use their strategy for non-discrete groups.

DOI: http://dx.doi.org/10.7900/jot.2017jan19.2147
Keywords: von Neumann algebras, subfactors, totally disconnected groups, Galois correspondence, Hecke pairs of groups

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