COALESCENCE OF CIRCLE EXTENSIONS OF MEASURE-PRESERVING TRANSFORMATIONS

We prove that for each ergodic automorphism T: (X, B, mu) --> (X, B, mu) for which we can find an element S is-an-element-of C(T) such that the corresponding Z2-action (S, T) on (X, B, mu) is free, there exists a circle valued cocycle phi such that the group extension T(phi) is ergodic but is not coalescent. In particular, the existence of such a cocycle is proved for all ergodic rigid automorphisms. As a corollary, in the class of ergodic transformations of [0, 1) x [0, 1) given by [GRAPHICS] for each irrational alpha we find phi such that T(phi) is not coalescent. In some special cases the group law of the centralizer is given.