Maximal subgroups and von Neumann subalgebras with the Haagerup property
Abstract
We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside and obtain several explicit instances where maximal Haagerup subgroups yield maximal Haagerup subalgebras. Our techniques are on one hand based on group-theoretic considerations, and on the other on certain results on intermediate von Neumann algebras, in particular these allowing us to deduce that all the intermediate algebras for certain inclusions arise from groups or from group actions. Some remarks and examples concerning maximal non-(T) subgroups and subalgebras are also presented, and we answer two questions of Ge regarding maximal von Neumann subalgebras.
Keywords
Cite
@article{arxiv.1903.08190,
title = {Maximal subgroups and von Neumann subalgebras with the Haagerup property},
author = {Yongle Jiang and Adam Skalski},
journal= {arXiv preprint arXiv:1903.08190},
year = {2021}
}
Comments
33 pages; v5 introduces several minor changes and updates the references. Accepted for publication in the Groups, Geometry and Dynamics