Homomorphisms of ergodic group actions and conjugacy of skew product actions

Abstract

Let G be a locally compact group acting ergodically on X. We discuss relationships between homomorphisms on the measured groupoid X×G, conjugacy of skew product extensions, and similarity of measured groupoids. To do this, we describe the structure of homomorphisms on X×G whose restriction to an extension given by a skew product action is the trivial homomorphism.