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A Galois type theorem in von Neumann algebras


Author: Hisashi Choda
Journal: Proc. Amer. Math. Soc. 115 (1992), 415-417
MSC: Primary 46L55; Secondary 46L40
DOI: https://doi.org/10.1090/S0002-9939-1992-1081090-8
MathSciNet review: 1081090
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Abstract: We shall give a simple proof for a Galois type theorem: Let $ \alpha $ be a dual free action of a discrete group $ {\text{G}}$ on a factor $ M$. If an automorphism $ \theta $ of $ M$ leaves the fixed point algebra $ {M^\alpha }$ pointwise invariant then there exists a $ {g_0} \in G$ with $ \theta = {\alpha _{{g_0}}}$.


References [Enhancements On Off] (What's this?)

  • [1] H. Choda, A Galois correspondence in a von Neumann algebra, Tôhoku Math. J. 30 (1978), 491-504. MR 516882 (80g:46052)
  • [2] -, An automorphism fixing the fixed point algebra of an automorphism group, Math. Japon. 24 (1979), 45-51. MR 539388 (80h:46108)
  • [3] M. Choda, Normal expectations and crossed products of von Neumann algebras, Proc. Japan Acad. 50 (1974), 738-742. MR 0372634 (51:8841)
  • [4] M. Henle, Galois theory of $ {W^*}$-algebras, preprint.
  • [5] K. Ikeshoji, A generalization of Roberts-Tannaka duality theorem, J. Math. Soc. Japan 34 (1982), 55-59. MR 639805 (83b:46081)
  • [6] Y. Katayama and M. Takesaki, Asymptotic Galois correspondence for discrete amenable actions on AFD factors, preprint.
  • [7] N. J. Munch, Conditional expectations and wandering operators for automorphic group actions, Math. Japon. 34 (1989), 65-72. MR 993243 (90d:46090)
  • [8] M. Nakamura and Z. Takeda, A Galois theory for finite factors, Proc. Japan Acad. 36 (1960), 258-260. MR 0123925 (23:A1246)
  • [9] Y. Nakagami and M. Takesaki, Duality for crossed products of von Neumann algebras, Lecture Notes in Math., vol. 731, Springer-Verlag, New York and Berlin, 1979. MR 546058 (81e:46053)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1081090-8
Keywords: Galois theory, von Neumann algebra, factor, action, expectation
Article copyright: © Copyright 1992 American Mathematical Society

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