Rigidity of group actions on homogeneous Spaces, III

Uri Bader; Alex Furman; Alex Gorodnik; Barak Weiss

doi:10.1215/00127094-2860021

Rigidity of group actions on homogeneous Spaces, III

Uri Bader, Alex Furman, Alex Gorodnik, Barak Weiss

Ben-Gurion University of the Negev, Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	115-155
Number of pages	41
Journal	Duke Mathematical Journal
Volume	164
Issue number	1
DOIs	https://doi.org/10.1215/00127094-2860021
State	Published - 1 Jan 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2860021

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title = "Rigidity of group actions on homogeneous Spaces, III",

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.",

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N2 - 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.

AB - 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.

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DO - 10.1215/00127094-2860021

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Rigidity of group actions on homogeneous Spaces, III

Abstract

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