On minimal strongly proximal actions of locally compact groups

Minimal, strongly proximal actions of locally compact
group G on compact spaces X, also known as *boundary actions*, were
introduced by Furstenberg in the study of Lie groups. In particular, the
action of a semi-simple real Lie group G on homogeneous spaces G/Q where
Q in G is a parabolic subgroup, are boundary actions. Countable discrete
groups admit a wide variety of boundary actions. In this note we show that
if X is a compact manifold with a faithful boundary action of some locally
compact group H, then (under some Holder regularity assumption) the group
H, the space X, and the action split into a direct product of a semi-simple
Lie group G acting on G/Q and a boundary action of a discrete countable
group.

Bibliographical: Israel J. Math.

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[Papers] [Alex Furman]