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Relative Entropy of a Fixed Point Algebra

  • Satoshi Kawakami
Part of the Progress in Mathematics book series (PM, volume 84)

Abstract

The relative entropy H(MN) for a pair NM of finite von Neumann algebras was introduced and studied by M. Pimsner and S.Popa in [7]. One of their important results was to clarify the relationship between H(MN) and the Jones index [M : N] for a pair of finite factors ([2]). On the other hand, in [1], V. Jones succeeded in classifying actions of a finite group G on the hyperfinite type II1 factor R, up to conjugacy, associated with normal subgroups of G, characteristic invariants and inner invariants.

Keywords

Normal Subgroup Finite Group Compact Group Relative Entropy Reduction Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    V. Jones, Actions of finite groups on the hyperfinite type II1 factor, Memoirs of A.M.S. 237 (1980).Google Scholar
  2. [2]
    V. Jones, Index of sub factors, Invention Math. 72 (1983), 1–25.MATHCrossRefGoogle Scholar
  3. [3]
    S. Kawakami and H. Yoshida, Actions of a finite group on finite von Neumann algebras and the relative entropy, J. Math. Soc. Japan 39 (1987), 609–626.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    S. Kawakami and H. Yoshida, Math. Japon., Reduction theory on the relative entropy, 33(1988), 975–990.MathSciNetMATHGoogle Scholar
  5. [5]
    G.W. Mackey, Unitary representations of group extensions I, Acta. Math. 99 (1958), 265–311.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    A. Ocneanu, Actions of discrete amenable groups on von Neumann algebras, Springer Lecture Notes, 1138 (1985).Google Scholar
  7. [7]
    M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. Éc. Norm. Sup. 19 (1986), 57–106.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Satoshi Kawakami
    • 1
  1. 1.Nara University of EducationNaraJapan

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