Duke Mathematical Journal

Rigidity of group actions on homogeneous spaces, III

Uri Bader, Alex Furman, Alex Gorodnik, and Barak Weiss

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Abstract

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice Γ acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors, and joinings defined a priori only in the measurable category are in fact algebraically constrained. Arguing in an elementary fashion, we manage to classify all the measurable Φ commuting with the Γ-action: assuming ergodicity, we find that they are algebraically defined.

Article information

Source
Duke Math. J., Volume 164, Number 1 (2015), 115-155.

Dates
First available in Project Euclid: 9 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1420813015

Digital Object Identifier
doi:10.1215/00127094-2860021

Mathematical Reviews number (MathSciNet)
MR3299103

Zentralblatt MATH identifier
1351.37011

Subjects
Primary: 37A17: Homogeneous flows [See also 22Fxx]
Secondary: 37A35: Entropy and other invariants, isomorphism, classification 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}

Keywords
lattices morphisms joinings algebraic groups homogeneous spaces

Citation

Bader, Uri; Furman, Alex; Gorodnik, Alex; Weiss, Barak. Rigidity of group actions on homogeneous spaces, III. Duke Math. J. 164 (2015), no. 1, 115--155. doi:10.1215/00127094-2860021. https://projecteuclid.org/euclid.dmj/1420813015


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