Journal article
Some OE- and W⁎-rigidity results for actions by wreath product groups
Journal of functional analysis, Vol.263(11), pp.3422-3448
12/01/2012
DOI: 10.1016/j.jfa.2012.08.025
Abstract
We use deformation-rigidity theory in the von Neumann algebra framework to study probability measure preserving actions by wreath product groups. In particular, we single out large families of wreath product groups satisfying various types of orbit equivalence (OE) rigidity. For instance, we show that whenever H, K, Γ, Λ are icc, property (T) groups such that H≀Γ and K≀Λ admit stably orbit equivalent action σ and ρ such that σ|Γ, ρ|Λ, σ|HΓ, and ρ|KΛ are ergodic, then automatically σΓ is stably orbit equivalent to ρΛ and σ|HΓ is stably orbit equivalent to ρ|KΛ. Rigidity results for von Neumann algebras arising from certain actions of such groups (i.e. W⁎-rigidity results) are also obtained.
Details
- Title: Subtitle
- Some OE- and W⁎-rigidity results for actions by wreath product groups
- Creators
- Ionut Chifan - Vanderbilt UniversitySorin Popa - University of California, Los AngelesJames Owen Sizemore - University of California, Los Angeles
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.263(11), pp.3422-3448
- DOI
- 10.1016/j.jfa.2012.08.025
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 12/01/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9984242347202771
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