Vanishing first cohomology and strong 1-boundedness for von Neumann algebras

DOI10.4171/jncg/530arXiv2110.12324MaRDI QIDQ6203830

Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli

Publication date: 8 April 2024

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.12324

zbMATH Keywords

free entropysofic groups\(\ell^2\)-Betti numbers\(\mathrm{II}_1\) factors

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) General theory of von Neumann algebras (46L10) Kazhdan's property (T), the Haagerup property, and generalizations (22D55)

Cites Work

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• Any generating set of an arbitrary property \(T\) von Neumann algebra has free entropy dimension \(\leq1\)
• The analogues of entropy and of Fisher's information measure in free probability theory. V: Noncommutative Hilbert transforms
• Applications of free entropy to finite von Neumann algebras. II
• The analogues of entropy and of Fisher's information measure in free probability theory. II
• Group cohomology, harmonic functions and the first \(L^ 2\)-Betti number
• Two applications of free entropy
• Large deviation bounds for matrix Brownian motion
• Rigidity of commensurators and irreducible lattices
• Orthogonal free quantum group factors are strongly 1-bounded
• Hyperlinearity, essentially free actions and \(L^2\)-invariants. The sofic property
• The analogues of entropy and of Fisher's information measure in free probability theory. III: The absence of Cartan subalgebras
• Duality for optimal couplings in free probability
• \(L^{2}\)-cohomology for von Neumann algebras
• Strongly 1-bounded von Neumann algebras
• Non-microstates free entropy dimension for groups
• Free transport for convex potentials
• 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
• Dimension theory of arbitrary modules over finite von Neumann algebras and L2-Betti numbers I: Foundations
• 1-Bounded entropy and regularity problems in von Neumann algebras
• Von Neumann algebras of sofic groups with β(2)1=0 are strongly 1-bounded
• Tracial smooth functions of non-commuting variables and the free Wasserstein manifold
• L²-homology for von Neumann algebras
• Formes linéaires sur un anneau d'opérateurs