We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside Z2⋊SL2(Z) 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.
Yongle Jiang; Adam Skalski. Maximal subgroups and von Neumann subalgebras with the Haagerup property. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 849-892. doi: 10.4171/ggd/614
@article{10_4171_ggd_614,
author = {Yongle Jiang and Adam Skalski},
title = {Maximal subgroups and von {Neumann} subalgebras with the {Haagerup} property},
journal = {Groups, geometry, and dynamics},
pages = {849--892},
year = {2021},
volume = {15},
number = {3},
doi = {10.4171/ggd/614},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/614/}
}
TY - JOUR
AU - Yongle Jiang
AU - Adam Skalski
TI - Maximal subgroups and von Neumann subalgebras with the Haagerup property
JO - Groups, geometry, and dynamics
PY - 2021
SP - 849
EP - 892
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/614/
DO - 10.4171/ggd/614
ID - 10_4171_ggd_614
ER -
%0 Journal Article
%A Yongle Jiang
%A Adam Skalski
%T Maximal subgroups and von Neumann subalgebras with the Haagerup property
%J Groups, geometry, and dynamics
%D 2021
%P 849-892
%V 15
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/614/
%R 10.4171/ggd/614
%F 10_4171_ggd_614
