Relative Entropy of a Fixed Point Algebra

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


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.


Normal Subgroup Finite Group Compact Group Relative Entropy Reduction Theory 
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    V. Jones, Actions of finite groups on the hyperfinite type II1 factor, Memoirs of A.M.S. 237 (1980).Google Scholar
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    V. Jones, Index of sub factors, Invention Math. 72 (1983), 1–25.MATHCrossRefGoogle Scholar
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    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
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    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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