Factors of ergodic group extensions of rotations

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Diagonal metric subgroups of the metric centralizer

C (T_{φ})

of group extensions are investigated. Any diagonal compact subgroup Z of

C (T_{φ})

is determined by a compact subgroup Y of a given metric compact abelian group X, by a family

{v_{y} : y \in Y}

, of group automorphisms and by a measurable function f:X → G (G a metric compact abelian group). The group Z consists of the triples

(y, F_{y}, v_{y})

, y ∈ Y, where

F_{y} (x) = v_{y} (f (x)) - f (x + y)

, x ∈ X.

group extension

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