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

• 成果类型: Article
• 署名作者: Popa, Sorin; Vaes, Stefaan
• 署名单位: University of California System; University of California Los Angeles; KU Leuven
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0110-9
• 发表日期: 2014
• 页码: 141-198
• 关键词: ergodic equivalence relations; measure space decomposition; w-rigid groups; malleable actions; STRUCTURAL THEORY; bernoulli actions; superrigidity; COHOMOLOGY; computations; INFINITY

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.