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

M.J. Borst

doi:10.4233/uuid:d63bdb80-fffa-4b97-85ba-7dc663e80721

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

M.J. Borst

Analysis

Research output: Thesis › Dissertation (TU Delft)

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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.

Original language	English
Awarding Institution	Delft University of Technology
Supervisors/Advisors	Caspers, M.P.T., Promotor Veraar, M.C., Promotor
Award date	24 Mar 2025
Print ISBNs	978-94-6384-727-8
DOIs	https://doi.org/10.4233/uuid:d63bdb80-fffa-4b97-85ba-7dc663e80721
Publication status	Published - 2025

Keywords

operator algebras
von Neumann algebras
deformation/rigidity theory
Coxeter groups
Hecke algebras
graph products
Strong solidity
Absence of Cartan subalgebras
Akemann-Ostrand property
Unique prime factorization (UPF)
Kurosh type theorems
Completely contractive approximation property (CCAP)
Commutator estimates
Derivations
quantum Markov semigroups

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

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.",

keywords = "operator algebras, von Neumann algebras, deformation/rigidity theory, Coxeter groups, Hecke algebras, graph products, Strong solidity, Absence of Cartan subalgebras, Akemann-Ostrand property, Unique prime factorization (UPF), Kurosh type theorems, Completely contractive approximation property (CCAP), Commutator estimates, Derivations, quantum Markov semigroups",

author = "M.J. Borst",

year = "2025",

doi = "10.4233/uuid:d63bdb80-fffa-4b97-85ba-7dc663e80721",

language = "English",

isbn = "978-94-6384-727-8",

type = "Dissertation (TU Delft)",

school = "Delft University of Technology",

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TY - THES

T1 - On rigidity theory, strong solidity, Coxeter groups, graph products and commutator estimates

AU - Borst, M.J.

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - operator algebras

KW - von Neumann algebras

KW - deformation/rigidity theory

KW - Coxeter groups

KW - Hecke algebras

KW - graph products

KW - Strong solidity

KW - Absence of Cartan subalgebras

KW - Akemann-Ostrand property

KW - Unique prime factorization (UPF)

KW - Kurosh type theorems

KW - Completely contractive approximation property (CCAP)

KW - Commutator estimates

KW - Derivations

KW - quantum Markov semigroups

U2 - 10.4233/uuid:d63bdb80-fffa-4b97-85ba-7dc663e80721

DO - 10.4233/uuid:d63bdb80-fffa-4b97-85ba-7dc663e80721

M3 - Dissertation (TU Delft)

SN - 978-94-6384-727-8

ER -

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

Abstract

Keywords

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