Dixmier problem in group theory

Target entity: Dixmier problem in group theory
Context triple: [Jacques Dixmier, notableConcept, Dixmier problem in group theory]

• A. Connes embedding problem
  The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
• B. L’intégration dans les groupes topologiques et ses applications
  L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
• C. Gel'fand–Kirillov conjecture
  The Gel'fand–Kirillov conjecture is a statement in noncommutative algebra proposing that certain universal enveloping algebras of Lie algebras are birationally equivalent to Weyl algebras, linking their structure to that of algebras of differential operators.
• D. Harmonic Analysis on Homogeneous Spaces
  Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
• E. Kesten’s theorem on random walks on groups
  Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Dixmier problem in group theory
Target entity description: The Dixmier problem in group theory is a famous open question asking whether every nontrivial finitely generated group has a nontrivial finite-dimensional unitary representation.

• A. Connes embedding problem
  The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
• B. L’intégration dans les groupes topologiques et ses applications
  L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
• C. Gel'fand–Kirillov conjecture
  The Gel'fand–Kirillov conjecture is a statement in noncommutative algebra proposing that certain universal enveloping algebras of Lie algebras are birationally equivalent to Weyl algebras, linking their structure to that of algebras of differential operators.
• D. Harmonic Analysis on Homogeneous Spaces
  Harmonic Analysis on Homogeneous Spaces is a mathematical monograph by Nolan Wallach that develops the theory of harmonic analysis and representation theory on Lie groups and their homogeneous spaces.
• E. Kesten’s theorem on random walks on groups
  Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
• F. None of above. chosen