Cohomology and extensions of Neumann algebras. I

DOI10.2977/prims/1195187501zbMath0462.46048OpenAlexW1999450329MaRDI QIDQ1153327

Colin E. Sutherland

Publication date: 1980

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195187501

zbMATH Keywords

cocycletwisted crossed productfixed point subalgebralifting automorphismsdual weightextensions of a von Neumann algebrafaithful semifinite weightlocally compact separable group of automorphismsprojective covariant system

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (19)

Rohlin flows on von Neumann algebras ⋮ CONTINUOUS FAMILIES OF HYPERFINITE SUBFACTORS WITH THE SAME STANDARD INVARIANT ⋮ Twisted actions and the obstruction to extending unitary representations of subgroups ⋮ Cohomology and extensions of von Neumann algebras. II ⋮ SUBFACTOR REALIZATION OF MODULAR INVARIANTS: II ⋮ Maximal von Neumann subalgebras arising from maximal subgroups ⋮ Normality of algebras over commutative rings and the Teichmüller class. III: Examples ⋮ Remarks on anomalous symmetries of \(C^*\)-algebras ⋮ A Characterization of Normal Extensions for Subfactors ⋮ Duality for crossed products of von Neumann algebras ⋮ Conformal orbifold theories and braided crossed \(G\)-categories ⋮ A Galois Correspondence for Reduced Crossed Products of Simple -algebras by Discrete Groups ⋮ Compact Abelian Prime Actions on Von Neumann Algebras ⋮ Structure of bicentralizer algebras and inclusions of type III factors ⋮ Actions of discrete amenable groups and groupoids on von Neumann algebras ⋮ Index pairings for \(\mathbb{R}^n\)-actions and Rieffel deformations ⋮ The operator quantization of the open bosonic string: Field algebra ⋮ On actions of amenable groups on \(II_ 1\)-factors ⋮ Maximal Abelian Subalgebras of von Neumann Algebras and Representations of Equivalence Relations

Cites Work

• Duality for crossed products and the structure of von Neumann algebras of type III
• Cohomology and extensions of von Neumann algebras. II
• A factor not anti-isomorphic to itself
• Automorphisms of full \(II_1\) factors, with applications to factors of type \(III\)
• The flow of weights on factors of type III
• Produits croises d'une \(C^ *\)-algèbre par un groupe d'automorphismes
• Point realizations of transformation groups
• Ergodic theory and virtual groups
• Tomita's theory of modular Hilbert algebras and its applications
• Virtual groups and group actions
• Cohomology theory in abstract groups. I
• On the extensions of finite factors, I
• The standard form of von Neumann algebras.
• Outer conjugacy classes of automorphisms of factors
• Group Extensions and Cohomology for Locally Compact Groups. III
• Une classification des facteurs de type ${\rm III}$
• Central Sequences and the Hyperfinite Factor
• Inner Product Modules Over B ∗ -Algebras

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