Structure of bicentralizer algebras and inclusions of type III factors

DOI10.1007/s00208-019-01939-9zbMath1451.46048arXiv1804.05706OpenAlexW2991063383MaRDI QIDQ2308327

Cyril Houdayer, Amine Marrakchi, Uffe Haagerup, Hiroshi Ando

Publication date: 3 April 2020

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.05706

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Noncommutative dynamical systems (46L55) Subfactors and their classification (46L37) States of selfadjoint operator algebras (46L30) Classification of factors (46L36)

Related Items (7)

Existentially closed \(\mathrm{W}^*\)-probability spaces ⋮ On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type \(\text{III}_1\) ⋮ Noncommutative ergodic theory of higher rank lattices ⋮ Ergodic states on type \(\mathrm{III}_1\) factors and ergodic actions ⋮ Full factors, bicentralizer flow and approximately inner automorphisms ⋮ Ozawa's class𝒮for locally compact groups and unique prime factorization of group von Neumann algebras ⋮ Connes' bicentralizer problem for q‐deformed Araki–Woods algebras

Cites Work

• Unnamed Item
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• Unique prime factorization and bicentralizer problem for a class of type III factors
• Factoriality, type classification and fullness for free product von Neumann algebras
• Semiregular maximal Abelian *-subalgebras and the solution to the factor state Stone-Weierstrass problem
• Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split \(W^*\)-inclusions
• Extension of Jones' theory on index of arbitrary factors
• Action of discrete amenable groups on von Neumann algebras
• Operator valued weights in von Neumann algebras. II
• Cohomology and extensions of Neumann algebras. I
• On a problem of R.V. Kadison on maximal Abelian *-subalgebras in factors
• Almost periodic states and factors of type III\(_1\)
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• The flow of weights on factors of type III
• Homogeneity of the state space of factors of type \(III_1\)
• A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras
• Fullness and Connes' \(\tau\) invariant of type III tensor product factors
• Pointwise inner automorphisms of von Neumann algebras. With an appendix by Colin Sutherland
• Index for subfactors
• On the relative Dixmier property for inclusions of \(C^*\)-algebras
• Full factors, bicentralizer flow and approximately inner automorphisms
• On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type \(\text{III}_1\)
• Singular MASAs in type III factors and Connes' bicentralizer property
• Ultraproducts of von Neumann algebras
• Asymptotic ratio set and property \(L_ \lambda^ \prime\)
• Conditional expectations in von Neumann algebras
• An analogue of Connes-Haagerup approach for classification of subfactors of the type III
• Product between ultrafilters and applications to the Connes' embedding problem
• Free Araki-Woods factors and Connes’ bicentralizer problem
• Entropy and index for subfactors
• The standard form of von Neumann algebras.
• The Equivalence of Various Definitions for a Properly Infinite Von Neumann Algebra to be Approximately Finite Dimensional
• Outer conjugacy classes of automorphisms of factors
• Canonical extension of endomorphisms of type III factors
• Une classification des facteurs de type ${\rm III}$
• Two finite, non‐hyperfinite, non‐isomorphic factors
• Asymptotic structure of free product von Neumann algebras

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