Journal article
RIGIDITY FOR VON NEUMANN ALGEBRAS OF GRAPH PRODUCT GROUPS II. SUPERRIGIDITY RESULTS
Journal of the Institute of Mathematics of Jussieu, Vol.24(1), pp.117-156
01/2025
DOI: 10.1017/S147474802400015X
Abstract
In [CDD22], we investigated the structure of $\ast $ -isomorphisms between von Neumann algebras $L(\Gamma )$ associated with graph product groups $\Gamma $ of flower-shaped graphs and property (T) wreath-like product vertex groups, as in [CIOS21]. In this follow-up, we continue the structural study of these algebras by establishing that these graph product groups $\Gamma $ are entirely recognizable from the category of all von Neumann algebras arising from an arbitrary nontrivial graph product group with infinite vertex groups. A sharper $C^*$ -algebraic version of this statement is also obtained. In the process of proving these results, we also extend the main $W^*$ -superrigidity result from [CIOS21] to direct products of property (T) wreath-like product groups.
Details
- Title: Subtitle
- RIGIDITY FOR VON NEUMANN ALGEBRAS OF GRAPH PRODUCT GROUPS II. SUPERRIGIDITY RESULTS
- Creators
- Ionuţ Chifan - University of IowaMichael Davis - University of IowaDaniel Drimbe - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of the Institute of Mathematics of Jussieu, Vol.24(1), pp.117-156
- Publisher
- CAMBRIDGE UNIV PRESS
- DOI
- 10.1017/S147474802400015X
- ISSN
- 1474-7480
- eISSN
- 1475-3030
- Number of pages
- 40
- Language
- English
- Electronic publication date
- 11/25/2024
- Date published
- 01/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984751757102771
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