L2-rigidity in von Neumann algebras

• 成果类型: Article
• 署名作者: Peterson, Jesse
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0154-6
• 发表日期: 2009
• 页码: 417-433
• 关键词: w-rigid groups; ii1 factors; malleable actions; CLASSIFICATION; COHOMOLOGY; entropy

摘要

We introduce the notion of L (2)-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L (2)-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property I, or are weakly rigid. As a consequence we obtain that if M is a free product of diffuse von Neumann algebras, or if M=LI where I is a finitely generated group with beta(1) ((2))(I)> 0, then any nonamenable regular subfactor of M is prime and does not have properties I or (T). In particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of N. Ozawa.