Dilations of Contraction Cocycles and Cocycle Perturbations of the Translation Group of the Line

The class of contraction cocycles which can be dilated to unitary Markovian cocycles of a translation group $S$ on the straight line is introduced. The class of cocycle perturbations of $S$ by unitary Markovian cocycles $W$ with the property $W_t-I\in\mathscr S_2$ (the Hilbert–Schmidt class) is investigated. The results are applied to perturbations of Kolmogorov flows on hyperfinite factors generated by the algebra of canonical anticommutation relations.