Weakly isomorphic transformations that are not isomorphic (Q1093235)

A new method for construction of transformations T: (X\({}_ i,{\mathcal B}_ i,\mu _ i)\), \(i=1,2\), that are factors of each other but that are not measure-theoretically isomorphic is provided. This method uses ergodic product cocycles of the form \(\phi \circ S^{i_ 1}\times \phi \circ S^{i_ 2}\times...\), where \(\phi\) : \(X\to Z_ 2\) is a cocycle, S belongs to the centralizer of T and T is an ergodic translation on a compact, monothetic group X.