International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 781-788

Homomorphisms of ergodic group actions and conjugacy of skew product actions

Edgar N. Reyes

Department of Mathematics, Southeastern Louisiana University, Hammond 70402, Louisiana, USA

Received 19 October 1994; Revised 1 June 1995

Copyright © 1996 Edgar N. Reyes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.