Rigidity for equivalence relations on homogeneous spaces

被引：3

作者：

Ioana, Adrian ^{[1
]}

Shalom, Yehuda ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

GROUPS GEOMETRY AND DYNAMICS | 2013年 / 7卷 / 02期

基金：

美国国家科学基金会;

关键词：

Relative property (T); homogenous spaces; II1; factors; equivalence relations; PROPERTY-T; II1; FACTORS;

D O I：

10.4171/GGD/187

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Popa's notion of rigidity for equivalence relations induced by actions on homogeneous spaces. For any lattices Gamma and Lambda in a semisimple Lie group G with finite center and no compact factors we prove that the action Gamma (sic) G/Lambda is rigid. If in addition G has property (T) then we derive that the von Neumann algebra L-infinity (G/Lambda) (sic) Gamma 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 Gamma (sic) G/Lambda is either hyperfinite or rigid.

引用

页码：403 / 417

页数：15