Preprint
Product rigidity in von Neumann and C∗-algebras via s-malleable deformations
arXiv.org
Cornell University
08/24/2021
DOI: 10.48550/arxiv.2012.04089
Abstract
We provide a new large class of countable icc groups A for which the product rigidity result from [CdSS15] holds: if Γ1,…,Γn∈A and Λ is any group such that L(Γ1×⋯×Γn)≅L(Λ), then there exists a product decomposition Λ=Λ1×⋯×Λn such that L(Λi) is stably isomorphic to L(Γi), for any 1≤i≤n. Class A consists of groups Γ for which L(Γ) admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups Γ such that either (a) Γ admits an unbounded 1-cocycle into its left regular representation, or (b) Γ is an arbitrary wreath product group with amenable base. As a byproduct of these results, we obtain new examples of W∗-superrigid groups and new rigidity results in the C∗-algebra theory.
Details
- Title: Subtitle
- Product rigidity in von Neumann and C∗-algebras via s-malleable deformations
- Creators
- Daniel Drimbe
- Resource Type
- Preprint
- Publication Details
- arXiv.org
- Publisher
- Cornell University; Ithaca, New York
- DOI
- 10.48550/arxiv.2012.04089
- eISSN
- 2331-8422
- Language
- English
- Date posted
- 08/24/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984696843402771
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