On rigidity theory, strong solidity, Coxeter groups, graph products and commutator estimates

Borst, Matthijs

On rigidity theory, strong solidity, Coxeter groups, graph products and commutator estimates

Doctoral thesis (2025)

Authors

Matthijs Borst Analysis

Contributors

M. Caspers Analysis (promotor)

Mark C. Veraar Analysis (promotor)

Research Group

Analysis

Von Neumann algebras Coxeter groups Operator algebras Strong solidity Akemann-Ostrand property Quantum Markov semigroups Completely contractive approximation property (CCAP) Commutator estimates Derivations Deformation/rigidity theory Hecke algebras Graph products Absence of Cartan subalgebras Unique prime factorization (UPF) Kurosh type theorems

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Published Date

2025

Language

English

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Research Group

Analysis

Abstract

The topic of this dissertation lies in the field of operator algebras and non-commutative functional analysis. The dissertation studies structural properties of C*-algebras and von Neumann algebras, with a focus on the latter. New rigidity results are obtain for von Neumann algebras coming from Coxeter groups and/or graph products. Furthermore, new results are obtained on approximation properties of von Neumann algebras and C*-algebras coming from graph products. Last, this dissertation obtains sharp estimates on the norms of commutators in factors.

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