On extension of cocycles

to normalizer elements, outer conjugacy,

and related problems

Authors:
Alexandre I. Danilenko and Valentin Ya. Golodets

Journal:
Trans. Amer. Math. Soc. **348** (1996), 4857-4882

MSC (1991):
Primary 46L55; Secondary 28D15, 28D99

DOI:
https://doi.org/10.1090/S0002-9947-96-01753-9

MathSciNet review:
1376544

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an ergodic automorphism of a Lebesgue space and a cocycle of with values in an Abelian locally compact group . An automorphism from the normalizer of the full group is said to be compatible with if there is a measurable function such that at a.e. . The topology on the set of all automorphisms compatible with is introduced in such a way that becomes a Polish group. A complete system of invariants for the -outer conjugacy (i.e. the conjugacy in the quotient group is found. Structure of the cocycles compatible with every element of is described.

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Additional Information

**Alexandre I. Danilenko**

Affiliation:
Department of Mechanics and Mathematics, Kharkov State University, Freedom Square 4, Kharkov, 310077, Ukraine

Email:
danilenko@ilt.kharkov.ua

**Valentin Ya. Golodets**

Affiliation:
Mathematics Department, Institute for Low Temperature Physics, Lenin Avenue 47, Kharkov, 310164, Ukraine

Email:
golodets@ilt.kharkov.ua

DOI:
https://doi.org/10.1090/S0002-9947-96-01753-9

Keywords:
Ergodic dynamical system,
cocycle,
outer conjugacy

Received by editor(s):
January 4, 1995

Additional Notes:
The work was supported in part by the International Science Foundation Grant No U2B000.

Article copyright:
© Copyright 1996
American Mathematical Society