Group measure space decomposition of II1 factors and W*-superrigidity

• 成果类型: Article
• 署名作者: Popa, Sorin; Vaes, Stefaan
• 署名单位: KU Leuven; University of California System; University of California Los Angeles
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0268-5
• 发表日期: 2010
• 页码: 371-417
• 关键词: malleable actions; strong rigidity; equivalence-relations; CLASSIFICATION; computations; COHOMOLOGY; INFINITY; index; rings

摘要

We prove a unique crossed product decomposition result for group measure space II1 factors L-infinity(X) (sic) Gamma arising from arbitrary free ergodic probability measure preserving (p. m. p.) actions of groups Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T-n denotes the group of upper triangular matrices in PSL(n, Z), then any free, mixing p. m. p. action of Gamma = PSL(n, Z) *T-n PSL(n, Z) is W*-superrigid, i.e. any isomorphism between L-infinity(X) (sic) Gamma and an arbitrary group measure space factor L infinity(Y) (sic) Lambda, comes from a conjugacy of the actions. We also prove that for many groups Gamma in the family G, the Bernoulli actions of Gamma are W*-superrigid.