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

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

Zbl 1131.46040
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