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Non-tame Lorentz actions of semisimple Lie groups

Published online by Cambridge University Press:  23 September 2003

SCOT ADAMS
SCOT ADAMS
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (e-mail: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 5 , October 2003 , pp. 1307 - 1322
Copyright
2003 Cambridge University Press

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