Induced and amenable ergodic actions of Lie groups
Robert J. Zimmer (1978)
Annales scientifiques de l'École Normale Supérieure
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Robert J. Zimmer (1978)
Annales scientifiques de l'École Normale Supérieure
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Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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Alexandre Danilenko (2000)
Colloquium Mathematicae
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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
Alexandre Danilenko, Toshihiro Hamachi (2000)
Colloquium Mathematicae
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The orbit equivalence of type 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 cocycles with values in Abelian groups.
Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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Raja, C.Robinson Edward (2009)
The New York Journal of Mathematics [electronic only]
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S. G. Dani (1984)
Compositio Mathematica
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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...
Robert J. Zimmer (1982)
Publications Mathématiques de l'IHÉS
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