Ergodic actions of semisimple Lie groups on compact principal bundles

Dave Witte; Robert J. Zimmer

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Ergodic actions of semisimple Lie groups on compact principal bundles

Dave Witte·Robert J. Zimmer

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Abstract

Let G = SL(n,R) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a volume-preserving, connection-preserving, ergodic action of G on some smooth, principal K-bundle P over M. Can M can be chosen independent of K? We show that if M = H/L is a homogeneous space, and the action of G on M is by translations, then P must also be a homogeneous space H'/L'. Consequently, there is a strong restriction on the groups K that can arise over this particular M.

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BibTeX RIS

Dave Witte, Robert J. Zimmer. 2002-05-30. Ergodic actions of semisimple Lie groups on compact principal bundles. https://arxiv.org/abs/math/0205323

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