2005/12/30 by Sorin Popa, Popa, Sorin · 1 citation
Mathematics · #20E05 #28D15 #46L10 #46L35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.math/0512646
openalex publication_date 2005/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if a countable discrete group Γ is \it w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. Γ= SL(2,\Bbb Z) \ltimes \Bbb Z2, or Γ= H × H' with H an infinite Kazhdan group and H' arbitrary), and \Cal V is a closed subgroup of the group of unitaries of a finite von Neumann algebra (e.g. \Cal V countable discrete, or separable compact), then any \Cal V-valued measurable cocycle for a measure preserving action Γ\curvearrowright X of Γ on a probability space (X,μ) which is weak mixing on H and \it s-malleable (e.g. the Bernoulli action Γ\curvearrowright [0,1]Γ) is cohomologous to a group morphism of Γ into \Cal V. We use the case \Cal V discrete of this result to prove that if in addition Γ has no non-trivial finite normal subgroups then any orbit equivalence between Γ\curvearrowright X and a free ergodic measure preserving action of a countable group Λ is implemented by a conjugacy of the actions, with respect to some group isomorphism Γ≃ Λ.