Preprint
Rigidity results for group von Neumann algebras with diffuse center
arXiv.org
Cornell University
03/02/2024
DOI: 10.48550/arxiv.2403.01280
Abstract
We introduce the first examples of groups G with infinite center which in a natural sense are completely recognizable from their von Neumann algebras, L(G). Specifically, assume that G=A×W, where A is an infinite abelian group and W is an ICC wreath-like product group [CIOS22a; AMCOS23] with property (T) and trivial abelianization. Then whenever H is an \emph{arbitrary} group such that L(G) is ∗-isomorphic to L(H), via an \emph{arbitrary} ∗-isomorphism preserving the canonical traces, it must be the case that H=B×H0 where B is infinite abelian and H0 is isomorphic to W. Moreover, we completely describe the ∗-isomorphism between L(G) and L(H). This yields new applications to the classification of group C∗-algebras, including examples of non-amenable groups which are recoverable from their reduced C∗-algebras but not from their von Neumann algebras.
Details
- Title: Subtitle
- Rigidity results for group von Neumann algebras with diffuse center
- Creators
- Ionuţ ChifanAdriana Fernández QueroHui Tan
- Resource Type
- Preprint
- Publication Details
- arXiv.org
- DOI
- 10.48550/arxiv.2403.01280
- eISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 03/02/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984568064502771
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