Non-tame Lorentz actions of semisimple Lie groups

Abstract

We show that if G is a connected semisimple Lie group with finite center, and if G admits a locally faithful, non-tame action by isometries of a connected Lorentz manifold, then $\mathfrak{g}$ has an ideal which is Lie algebra isomorphic to $\mathfrak{sl}_2(\mathbb{R})$ . We also analyze the collection of connected Lie groups G admitting a free action by isometries of a connected Lorentz manifold such that the action is properly ergodic with respect to the Lorentz volume form.