Isomorphic Actions of Group Extensions on a Measure Space

Abstract

Let E = E(G, A) be a group extension of an abelian 1.c.s.c. group A by an amenable 1.c.s.c. group G. An ergodic action V of A is said to be extendible to an action W of E if V(A) is isomorphic to the restriction of W onto the subgroup A C E. The extension property is described and studied in terms of cocycles over a skew product with values in A. Several examples of R-actions are considered. We answer the question of when two isomorphic actions of A can be extended to isomorphic actions of E(G,A).