Isometric extensions, 2-cocycles and ergodicity of skew products
Volume 137 / 1999
Studia Mathematica 137 (1999), 123-142
DOI: 10.4064/sm-137-2-123-142
Abstract
We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension $T_α$ and admits a prescribed subgroup in the centralizer of $T_α$.
