Logo image
Some OE- and W⁎-rigidity results for actions by wreath product groups
Journal article   Open access   Peer reviewed

Some OE- and W⁎-rigidity results for actions by wreath product groups

Ionut Chifan, Sorin Popa and James Owen Sizemore
Journal of functional analysis, Vol.263(11), pp.3422-3448
12/01/2012
DOI: 10.1016/j.jfa.2012.08.025
url
https://doi.org/10.1016/j.jfa.2012.08.025View
Published (Version of record) Open Access

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.
von Neumann algebras

Details

Metrics

Logo image