W∗-superrigidity for coinduced actions

Abstract

We prove W * -superrigidity for a large class of coinduced actions. We prove that if Σ is an amenable almost-malnormal subgroup of an infinite conjugagy class (icc) property (T) countable group Γ, the coinduced action Γ X from an arbitrary probability measure preserving action Σ X0 is W * -superrigid. We also prove a similar statement if Γ is an icc non-amenable group which is measure equivalent to a product of two infinite groups. In particular, we obtain that any Bernoulli action of such a group Γ is W * -superrigid. DANIEL DRIMBEThe main ingredient of his proof was the discovery of a beautiful dichotomy result for abelian subalgebras of II 1 factors coming from Bernoulli actions.

Cocycle superrigidity for profinite actions of irreducible lattices

“…The first families of W -superrigid actions were discovered about 10 years ago [19,31,36]. Since then, many other families of W -superrigid actions have been found (see the introduction of [5]).…”