Journal article
Some rigidity results for II1 factors arising from wreath products of property (T) groups
Journal of Functional Analysis, Vol.278(7), 108419
2020
DOI: 10.1016/j.jfa.2019.108419
Abstract
We show that any infinite collection (Γn)n∈N of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic infinite product rigidity phenomenon. If Λ is an arbitrary group such that L(⊕n∈NΓn)≅L(Λ) then there exists an infinite direct sum decomposition Λ=(⊕n∈NΛn)⊕A with A icc amenable or trivial such that, for all n∈N, up to amplifications, we have L(Γn)≅L(Λn) and L(⊕k≥nΓk)≅L((⊕k≥nΛk)⊕A). The result is sharp and complements the previous finite product rigidity property found in [16]. Using this we provide an uncountable family of restricted wreath products Γ≅Σ≀Δ of icc, property (T) groups Σ, Δ whose wreath product structure is recognizable, up to a normal amenable subgroup, from their von Neumann algebras L(Γ). Along the way we highlight several applications of these results to the study of rigidity in the C⁎-algebra setting. © 2019 Elsevier Inc.
Details
- Title: Subtitle
- Some rigidity results for II1 factors arising from wreath products of property (T) groups
- Creators
- Ionut Chifan - University of IowaBogdan Teodor Udrea - Romanian Academy
- Resource Type
- Journal article
- Publication Details
- Journal of Functional Analysis, Vol.278(7), 108419
- DOI
- 10.1016/j.jfa.2019.108419
- ISSN
- 0022-1236
- Publisher
- Academic Press Inc.
- Grant note
- Funding text 1: I.C. was supported by NSF Grant DMS #1600688.
- Language
- English
- Date published
- 2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984230407902771
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