6533b822fe1ef96bd127d5b0
RESEARCH PRODUCT
Extensions of cocycles for hyperfinite actions and applications
P. GabrielKlaus SchmidtMariusz Lemańczyksubject
CombinatoricsGroup extensionGeneral MathematicsErgodic theoryCountable setStandard probability spaceAutomorphismEquivalence (measure theory)Hyperfinite setCentralizer and normalizerMathematicsdescription
Given a countable, hyperfinite, ergodic and measure-preserving equivalence relationR on a standard probability space (X, ℬ, μ) and an elementW of the normalizerN (R) ofR, we investigate the problem of extendingR-cocycles to\(\bar R\), where\(\bar R\) is the relation generated byR andW. As an application, we obtain that for a Bernoulli automorphism the smallest family of natural factors in sense of [6] consists of all factors. Given an automorphism which is embeddable in a measurable flow and a compact, metric group, we show that for a typical cocycle we cannot lift the whole flow to the centralizer of the corresponding group extension.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-09-01 | Monatshefte für Mathematik |