Journal article
Amalgamated free product rigidity for group von Neumann algebras
Advances in mathematics (New York. 1965), Vol.329, pp.819-850
04/30/2018
DOI: 10.1016/j.aim.2018.02.025
Abstract
We provide a fairly large family of amalgamated free product groups Γ=Γ1⁎ΣΓ2 whose amalgam structure can be completely recognized from their von Neumann algebras. Specifically, assume that Γi is a product of two icc non-amenable bi-exact groups, and Σ is icc amenable with trivial one-sided commensurator in Γi, for every i=1,2. Then Γ satisfies the following rigidity property: any group Λ such that L(Λ) is isomorphic to L(Γ) admits an amalgamated free product decomposition Λ=Λ1⁎ΔΛ2 such that the inclusions L(Δ)⊆L(Λi) and L(Σ)⊆L(Γi) are isomorphic, for every i=1,2. This result significantly strengthens some of the previous Bass–Serre rigidity results for von Neumann algebras. As a corollary, we obtain the first examples of amalgamated free product groups which are W⁎-superrigid.
Details
- Title: Subtitle
- Amalgamated free product rigidity for group von Neumann algebras
- Creators
- Ionuţ Chifan - Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USAAdrian Ioana - Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
- Resource Type
- Journal article
- Publication Details
- Advances in mathematics (New York. 1965), Vol.329, pp.819-850
- DOI
- 10.1016/j.aim.2018.02.025
- ISSN
- 0001-8708
- eISSN
- 1090-2082
- Publisher
- Elsevier Inc
- Grant note
- 1600688; 1301370 / NSF (https://doi.org/10.13039/100000001) FG-BR2013-045 / Sloan Foundation Fellowship 1253402 / NSF (https://doi.org/10.13039/100000001)
- Language
- English
- Date published
- 04/30/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9983985882302771
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