Proper actions on strongly regular homogeneous spaces

Let $G/H$ be a strongly regular homogeneous space such that $H$ is a Lie group of inner type. We show that $G/H$ admits a proper action of a discrete non-virtually abelian subgroup of $G$ if and only if $G/H$ admits a proper action of a subgroup $L \subset G$ locally isomorphic to $SL(2, \mathbb{R})$. We classify all such spaces.

Keywords

proper actions, homogeneous spaces, Lie groups

2010 Mathematics Subject Classification

22E40, 22F30, 57S30

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Received 2 February 2016

Accepted 23 September 2016

Published 6 March 2018