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Wreath-like products of groups and their von Neumann algebras II: Outer automorphisms

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arxiv 2304.07457 v3 pith:QMUHC3HJ submitted 2023-04-15 math.OA math.GR

I. Chifan , A. Ioana , D. Osin , B. Sun This is my paper · ORCID
classification math.OAmath.GR
keywords groupcongcountablegroupsneumannpropertytextalgebra
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abstract

Given a countable group $G$, let ${\rm L}(G)$ denote its von Neumann algebra. For a wide class of ICC groups with Kazhdan's property (T), we confirm a conjecture of V.F.R. Jones asserting that $Out(\text{L}(G))\cong Char (G)\rtimes Out(G)$. As an application, we show that, for every countable group $Q$, there exists an ICC group $G$ with property (T) such that $Out(\text{L}(G))\cong Q$.

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  1. A continuum of non-measure equivalent groups

    math.GR 2025-12 conditional novelty 7.0 of 10

    A continuum of pairwise non-measure-equivalent finitely generated property (T) groups with all ℓ²-Betti numbers zero is constructed.

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