Maximal von Neumann subalgebras arising from maximal subgroups

Ge (2003) asked the question whether LF ∞ can be embedded in to LF 2 as a maximal subfactor. We answer it affirmatively in three different approaches, all containing the same key ingredient: the existence of maximal subgroups with infinite index. We also show that point stabilizer subgroups for ever...

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Bibliographic Details
Published inScience China. Mathematics Vol. 64; no. 10; pp. 2295 - 2312
Main Author Jiang, Yongle
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.10.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Subgroups
maximal von Neumann subalgebra
20B22
highly transitive action
maximal subfactor
maximal subgroup
rigid subalgebra
46L10
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Summary:Ge (2003) asked the question whether LF ∞ can be embedded in to LF 2 as a maximal subfactor. We answer it affirmatively in three different approaches, all containing the same key ingredient: the existence of maximal subgroups with infinite index. We also show that point stabilizer subgroups for every faithful, 4-transitive action on an infinite set give rise to maximal von Neumann subalgebras. By combining this with the known results on constructing faithful, highly transitive actions, we get many maximal von Neumann subalgebras arising from maximal subgroups with infinite index.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-020-1671-9