A class of superrigid group von Neumann algebras

• 成果类型: Article
• 署名作者: Ioana, Adrian; Popa, Sorin; Vaes, Stefaan
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.1.4
• 发表日期: 2013
• 页码: 231-286
• 关键词: w-rigid groups; ii1 factors; malleable actions; bernoulli actions; free-products; property-t; rings; CLASSIFICATION; computations; hyperfinite

摘要

We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely remembers the group G. More precisely, if L(G) is isomorphic to the von Neumann algebra L Lambda of an arbitrary countable group Lambda, then Lambda must be isomorphic to G. This represents the first superrigidity result pertaining to group von Neumann algebras.