Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups

被引：75

作者：

Popa, Sorin ^{[1
]}

Vaes, Stefaan ^{[2
]}

机构：

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

[2] Katholieke Univ Leuven, Dept Math, BE-3001 Louvain, Belgium

来源：

ACTA MATHEMATICA | 2014年 / 212卷 / 01期

基金：

比利时弗兰德研究基金会;

关键词：

ERGODIC EQUIVALENCE RELATIONS; MEASURE SPACE DECOMPOSITION; W-RIGID GROUPS; MALLEABLE ACTIONS; STRUCTURAL THEORY; BERNOULLI ACTIONS; SUPERRIGIDITY; COHOMOLOGY; COMPUTATIONS; INFINITY;

D O I：

10.1007/s11511-014-0110-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for any free ergodic probability measure-preserving action of a free group on n generators , the associated group measure space II1 factor has L (a)(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II1 factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II1 factors arising from arbitrary actions of a much larger family of groups, including all free products of amenable groups and their direct products.

引用

页码：141 / 198

页数：58

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