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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 643–660 (Mi izv1523)  

This article is cited in 1 scientific paper (total in 1 paper)

Outer conjugacy of the actions of countable amenable groups on a measure space

S. I. Bezuglyi, V. Ya. Golodets


Abstract: The following assertion is proved. Let $T$ be an automorphism of a Lebesgue space $(X,\mu)$, preserving the (finite or infinite) measure $\mu$, and let $U_i(G)$, $i=1,2$, be actions of a countable amenable group $G$ by automorphisms on $(X,\mu)$, such that $U_i(G)\subset N[T]$, where $N[T]$ is the normalizer of the full group $[T]$. For the existence of an automorphism $\theta\in N[T]$ such that $U_1(g)=\theta^{-1}U_2(g)t\theta$ (the outer conjugacy of the actions $U_1$ and $U_2$), where $t=t(g)\in[T]$, $g\in G$, it is necessary and sufficient that
\begin{gather*} \{g\in G:U_1(g)\in[T]\}=\{g\in G:U_2(g)\in[T]\},
\frac{d\mu\circ U_1(g)}{d\mu}=\frac{d\mu\circ U_2(g)}{d\mu}\quad(g\in G). \end{gather*}
The proof uses properties of cocycles of approximable groups of automorphisms.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 1–18

Bibliographic databases:

UDC: 517+519.46
MSC: Primary 28D15; Secondary 46L10
Received: 14.03.1984

Citation: S. I. Bezuglyi, V. Ya. Golodets, “Outer conjugacy of the actions of countable amenable groups on a measure space”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 643–660; Math. USSR-Izv., 29:1 (1987), 1–18

Citation in format AMSBIB
\Bibitem{BezGol86}
\by S.~I.~Bezuglyi, V.~Ya.~Golodets
\paper Outer conjugacy of the actions of countable amenable groups on a~measure space
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 643--660
\mathnet{http://mi.mathnet.ru/izv1523}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=864169}
\zmath{https://zbmath.org/?q=an:0636.28009}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 1--18
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000906}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. S. Veksler, A. L. Fëdorov, “Conjugacy of homomorphisms of locally compact groups into the outer group of measurable equivalence relation”, Funct. Anal. Appl., 22:4 (1988), 318–319  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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