On Popa’s cocycle superrigidity theorem. (English) Zbl 1134.46043

Furman, Alex

Int. Math. Res. Not. 2007, No. 19, Article ID rnm073, 46 p. (2007).

Summary: These notes contain an ergodic-theoretic account of the cocycle superrigidity theorem recently discovered by Sorin Popa [cf. S. Popa, Invent. Math. 170, No. 2, 243–295 (2007; Zbl 1131.46040)]. We state and prove a relative version of the result, discuss some applications to measurable equivalence relations, and point out that Gaussian actions (of “rigid” groups) satisfy the assumptions of Popa’s theorem.

MSC:

46L55	Noncommutative dynamical systems
37A20	Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
46L35	Classifications of \(C^*\)-algebras
22D25	\(C^*\)-algebras and \(W^*\)-algebras in relation to group representations

Citations:

Zbl 1131.46040