Factors of ergodic group extensions of rotations
Volume 103 / 1992
Studia Mathematica 103 (1992), 123-131
DOI: 10.4064/sm-103-2-123-131
Abstract
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 ${v_y : y ∈ Y}$, 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.
