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Locally compact groups appearing as ranges of cocycles of ergodic ℤ-actions

Published online by Cambridge University Press:  19 September 2008

V. Ya. Golodets  and
S. D. Sinelshchikov
V. Ya. Golodets
Affiliation:
Institute of Low Temperature Physics and Engineering, UkrSSR Academy of Sciences, 47 Lenin Ave, Kharkov 310164, USSR
S. D. Sinelshchikov
Affiliation:
Institute of Low Temperature Physics and Engineering, UkrSSR Academy of Sciences, 47 Lenin Ave, Kharkov 310164, USSR
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Abstract

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The paper contains the proof of the fact that every solvable locally compact separable group is the range of a cocycle of an ergodic automorphism. The proof is based on the theory of representations of canonical anticommutation relations and the orbit theory of dynamical systems. The slight generalization of reasoning shows further that this result holds for amenable Lie groups as well and can be also extended to almost connected amenable locally compact separable groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 47 - 57
Copyright
Copyright © Cambridge University Press 1985

References

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