The structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions
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Publication:1201277
DOI10.1007/BF02392758zbMath0781.46047OpenAlexW2085026304WikidataQ114233827 ScholiaQ114233827MaRDI QIDQ1201277
Yasuyuki Kawahigashi, Masamichi Takesaki, Colin E. Sutherland
Publication date: 17 January 1993
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392758
approximately finite-dimensional factors of type IIIapproximately inner automorphismscentrally trivial automorphismsextended modular automorphismRohlin's lemma
General theory of von Neumann algebras (46L10) Classifications of (C^*)-algebras (46L35) Automorphisms of selfadjoint operator algebras (46L40)
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Cites Work
- Unnamed Item
- Actions of discrete amenable groups on injective factors of type \(III_{\lambda}\), \(\lambda\) \(\neq 1\)
- Actions of compact Abelian groups on semifinite injective factors
- Action of discrete amenable groups on von Neumann algebras
- Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\)
- Compact Abelian group actions on injective factors
- Almost periodic states and factors of type III\(_1\)
- Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
- Measure space automorphisms, the normalizers of their full groups, and approximate finiteness
- The flow of weights on factors of type III
- Homogeneity of the state space of factors of type \(III_1\)
- Pointwise inner automorphisms of von Neumann algebras. With an appendix by Colin Sutherland
- Actions of discrete amenable groups and groupoids on von Neumann algebras
- Asymptotic ratio set and property \(L_ \lambda^ \prime\)
- A Construction of Approximately Finite-Dimensional Non-ITPFI Factors
- Actions of finite groups on the hyperfinite type 𝐼𝐼₁ factor
- Outer conjugacy classes of automorphisms of factors
- Une classification des facteurs de type ${\rm III}$