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RIGIDITY FOR VON NEUMANN ALGEBRAS OF GRAPH PRODUCT GROUPS II. SUPERRIGIDITY RESULTS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  25 November 2024

Ionuţ Chifan ,
Michael Davis  and
Daniel Drimbe Open the ORCID record for Daniel Drimbe [Opens in a new window]
Ionuţ Chifan
Affiliation:
14 MacLean Hall, Department of Mathematics, The University of Iowa, IA, 52242, USA ionut-chifan@uiowa.edu
Michael Davis
Affiliation:
14 MacLean Hall, Department of Mathematics, The University of Iowa, IA, 52242, USA michael-l-davis@uiowa.edu
Daniel Drimbe*
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK 14 MacLean Hall, Department of Mathematics, The University of Iowa, IA, 52242
*
danidrimbe@gmail.com
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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.

Keywords

von Neumann algebrasgraph product of groupsproduct rigiditysuperrigidity

MSC classification

Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L36: Classification of factors
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 24 , Issue 1 , January 2025 , pp. 117 - 156
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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