Hyperfinite Factors and Amenable Ergodic Actions.
Robert J. Zimmer (1977)
Inventiones mathematicae
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Robert J. Zimmer (1977)
Inventiones mathematicae
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Antony Wassermann (1988)
Inventiones mathematicae
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Calvin C. Moore, Robert J. Zimmmer (1979)
Inventiones mathematicae
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Sergio Alberverio, Raphael Hoegh-Krohn (1980)
Mathematische Zeitschrift
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Shahar Mozes (1992)
Inventiones mathematicae
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Shahar Mozes (1995)
Inventiones mathematicae
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Robert J. Zimmer (1978)
Annales scientifiques de l'École Normale Supérieure
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Artur Siemaszko (1994)
Studia Mathematica
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Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.
Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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Pierre Fima (2014)
Annales de l’institut Fourier
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We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.