Orbit equivalence and rigidity of ergodic actions of Lie groups

1 June 1981

journal article
research article
Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems

Vol. 1 (2) , 237-253
https://doi.org/10.1017/s0143385700009251

Abstract

The rigidity theorem for ergodic actions of semi-simple groups and their lattice subgroups provides results concerning orbit equivalence of the actions of these groups with finite invariant measure. The main point of this paper is to extend the rigidity theorem on one hand to actions of general Lie groups with finite invariant measure, and on the other to actions of lattices on homogeneous spaces of the ambient connected group possibly without invariant measure. For example, this enables us to deduce non-orbit equivalence results for the actions of SL (n, ℤ) on projective space, Euclidean space, and general flag and Grassman varieties.

Keywords

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