Maximal subgroups and von Neumann subalgebras with the Haagerup property

We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside [Z.sup.2] [??] [SL.sub.2](Z) and obtain several explicit instances where maximal Haagerup subgroups yield maximal Haagerup subalgebras. Our te...

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Bibliographic Details
Published inGroups, geometry and dynamics Vol. 15; no. 3; pp. 849 - 892
Main Authors Jiang, Yongle, Skalski, Adam
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
Subjects
Group actions (Mathematics)
Mathematical research
Topological groups
Von Neumann algebras
Poland
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Summary:We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside [Z.sup.2] [??] [SL.sub.2](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. Mathematics Subject Classification (2020). Primary: 46L10; Secondary: 20E28,22D25. Keywords. Von Neumann algebras, Haagerup property, maximal subgroups/subalgebras.
ISSN:1661-7207
1661-7215
DOI:10.4171/ggd/614