Journal article
Weak Equivalence and the Structures of Cocycles of an Ergodic Automorphism
Publications of the Research Institute for Mathematical Sciences, Vol.27(4), pp.577-625
1991
DOI: 10.2977/prims/1195169421
Abstract
Let (X, μ) be a Lebesgue space, Γ an approximately finite ergodic group of the automorphisms, α a cocycle on X×Γ with values in an arbitrary abelian l.c.s. group G, and ρ the Radon-Nikodym cocycle X×Γ. The concept of weak equivalence of the pairs (Γ, α) is introduced and studied, which generalizes the concept of trajectory equivalence of automorphism groups. It is proved that the pairs (Γ1, α01) and (Γ2, α02) (α0i=(α, ρ)) are (stably) weakly equivalent iff the corresponding Mackey pairs W1(G0) and W2(G0) of the group G0=G×R are isomorphic. It is proved that any ergodic action of G×R (or G) is isomorphic to the Mackey action associated with a certain pair (Γ, α0). The structure of cocycles of approximately finite equivalence relations is studied. The relationship between the type of the group Γ and that of the corresponding Mackey action is considered.
Details
- Title: Subtitle
- Weak Equivalence and the Structures of Cocycles of an Ergodic Automorphism
- Creators
- Sergey I BezuglyiValentin Ya Golodets
- Resource Type
- Journal article
- Publication Details
- Publications of the Research Institute for Mathematical Sciences, Vol.27(4), pp.577-625
- DOI
- 10.2977/prims/1195169421
- ISSN
- 0034-5318
- eISSN
- 1663-4926
- Language
- English
- Date published
- 1991
- Academic Unit
- Mathematics
- Record Identifier
- 9983985849602771
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