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Orbit equivalence and rigidity of ergodic actions of Lie groups

Published online by Cambridge University Press:  19 September 2008

Robert J. Zimmer
Robert J. Zimmer*
Affiliation:
From the Department of Mathematics, University of Chicago, USA
*
†Address for correspondence: Dr Robert J. Zimmer, Department of Mathematics, University of Chicago, Chicago, III. 60637, USA.
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 237 - 253
Copyright
Copyright © Cambridge University Press 1981

References

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