W∗-superrigidity for coinduced actions

Abstract

We prove W[Formula: see text]-superrigidity for a large class of coinduced actions. We prove that if [Formula: see text] is an amenable almost-malnormal subgroup of an infinite conjugagy class (icc) property (T) countable group [Formula: see text], the coinduced action [Formula: see text] from an arbitrary probability measure preserving action [Formula: see text] is W[Formula: see text]-superrigid. We also prove a similar statement if [Formula: see text] 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 [Formula: see text] is W[Formula: see text]-superrigid.