We study Popa's notion of rigidity for equivalence relations induced by actions on homogeneous spaces. For any lattices Γ and Λ in a semisimple Lie group G with finite center and no compact factors we prove that the action Γ↷G/Λ is rigid. If in addition G has property (T) then we derive that the von Neumann algebra L∞(G/Λ)⋊Γ has property (T). We also show that if the stabilizer of any non-zero point in the Lie algebra of G under the adjoint action of G is amenable (e.g., if G=SL2(R)), then any ergodic subequivalence relation of the orbit equivalence relation of the action Γ↷G/Λ is either hyperfinite or rigid.
1
University of California, San Diego, United States
2
Tel Aviv University, Israel
Adrian Ioana; Yehuda Shalom. Rigidity for equivalence relations on homogeneous spaces. Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 403-417. doi: 10.4171/ggd/187
@article{10_4171_ggd_187,
author = {Adrian Ioana and Yehuda Shalom},
title = {Rigidity for equivalence relations on homogeneous spaces},
journal = {Groups, geometry, and dynamics},
pages = {403--417},
year = {2013},
volume = {7},
number = {2},
doi = {10.4171/ggd/187},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/187/}
}
TY - JOUR
AU - Adrian Ioana
AU - Yehuda Shalom
TI - Rigidity for equivalence relations on homogeneous spaces
JO - Groups, geometry, and dynamics
PY - 2013
SP - 403
EP - 417
VL - 7
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/187/
DO - 10.4171/ggd/187
ID - 10_4171_ggd_187
ER -
%0 Journal Article
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%A Yehuda Shalom
%T Rigidity for equivalence relations on homogeneous spaces
%J Groups, geometry, and dynamics
%D 2013
%P 403-417
%V 7
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/187/
%R 10.4171/ggd/187
%F 10_4171_ggd_187
