Displaying similar documents to “On subrelations of ergodic measured type III equivalence relations”

On measure theoretical analogues of the Takesaki structure theorem for type III factors

Alexandre Danilenko, Toshihiro Hamachi (2000)

Colloquium Mathematicae

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The orbit equivalence of type I I I 0 ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type I I I 0 cocycles with values in Abelian groups.

A property of ergodic flows

Maria Joiţa, Radu-B. Munteanu (2014)

Studia Mathematica

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We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III₀ whose associated flow has this property is not of product type. A consequence is that a properly ergodic flow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which-up to conjugacy-is built under a function with the dyadic odometer as base automorphism.

Construction of non-constant and ergodic cocycles

Mahesh Nerurkar (2000)

Colloquium Mathematicae

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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...

Isometric extensions, 2-cocycles and ergodicity of skew products

Alexandre Danilenko, Mariusz Lemańczyk (1999)

Studia Mathematica

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We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension T α and admits a prescribed subgroup in the centralizer of T α .