Work

Rigidity for Von Neumann Algebras of Graph Product Groups Ii. Superrigidity Results

Year: 2024

Type: article

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.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s147474802400015x

Authors: Ionuţ Chifan, Michael Davis, Daniel Drimbe

Institutions: University of Iowa, University of Oxford

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fonds Wetenschappelijk Onderzoek, Vlaamse regering

Awards: Rigidity and structural results in von Neumann algebras and Ergodic Theory, G6282227863, Classification of von Neumann Algebras: Connections and Applications to C*-algebras, Geometric Group Theory and Continuous Model Theory, FRG: Collaborative Research: von Neumann Algebras Associated to Groups Acting on Hyperbolic Spaces