On extension of cocycles to normalizer elements, outer conjugacy, and related problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On extension of cocycles to normalizer elements, outer conjugacy, and related problems

Authors:	Alexandre I Danilenko Valentin Ya Golodets

Institution:	Department of Mechanics and Mathematics, Kharkov State University, Freedom Square 4, Kharkov, 310077, Ukraine ; Mathematics Department, Institute for Low Temperature Physics, Lenin Avenue 47, Kharkov, 310164, Ukraine

Abstract:	Let be an ergodic automorphism of a Lebesgue space and $\alpha$ a cocycle of with values in an Abelian locally compact group . An automorphism $\theta$ from the normalizer of the full group is said to be compatible with $\alpha$ if there is a measurable function $\varphi : X \to G$ such that $\alpha (\theta x, \theta T\theta ^{-1}) = - \varphi (x) + \alpha (x, T) + \varphi (Tx)$ at a.e. . The topology on the set $D(T, \alpha )$ of all automorphisms compatible with $\alpha$ is introduced in such a way that $D(T , \alpha )$ becomes a Polish group. A complete system of invariants for the $\alpha$ -outer conjugacy (i.e. the conjugacy in the quotient group $D(T, \alpha )/T])$ is found. Structure of the cocycles compatible with every element of is described.

Keywords:	Ergodic dynamical system cocycle outer conjugacy

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