Uniform subgroups and ergodic actions of exponential Lie groups

Robert Jeffrey Zimmer

Vol. 78 (1978), No. 1, 267–272

DOI: 10.2140/pjm.1978.78.267

Abstract

We show that the restriction of an ergodic action of an exponential solvable Lie group to a uniform subgroup is still ergodic provided that the restriction to the commutator subgroup is ergodic. This complements similar results previously obtained for semi-simple and nilpotent Lie groups.

Mathematical Subject Classification 2000

Primary: 22D40

Secondary: 28D15

Milestones

Received: 21 February 1978

Published: 1 September 1978