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Endomorphisms and Automorphisms for Factor Inclusions

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Quantum and Non-Commutative Analysis

Part of the book series: Mathematical Physics Studies ((MPST,volume 16))

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Abstract

We investigate some kinds of *;-endomorphisms and automorphisms for inclusions of type II1 factors in connection with Jones index theory.

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References

  1. J. Bion-Nadal, Subfactors of the hyperfinite II1 factor with Coxeter graph E6 as invariant, Current topics in Operator algebras, World Scientific, (1991).

    Google Scholar 

  2. O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. amer. Math. Soc., 171, 195–234 (1972).

    MathSciNet  MATH  Google Scholar 

  3. M. Choda, Shifts on the hyperfinite II1-factor, J. Operator Theory, 17, 223–235 (1987).

    MathSciNet  MATH  Google Scholar 

  4. M. Choda, Entropy for *;-endomorphisms and relative entropy for subalgebras, to appear in J. Operator Theory.

    Google Scholar 

  5. M. Choda, Entropy for Canonical shifts, to appear in Trans. Amer. Math. Soc..

    Google Scholar 

  6. M. Choda and F. Hiai, Entropy for canonical shifts II, Publ., RIMS, Kyoto Univ., 27, 461–489 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Choda, Duality for finite bipartite graphs (with an application to II1 factors), to appear in Pacific J. Math..

    Google Scholar 

  8. M. Choda, Square roots of the canonical shifts, Preprint.

    Google Scholar 

  9. A. Connes and E. Stormer, Entropy for automorphism of II1 von Neumann algebras, Acta Math., 134, 288–306 (1975).

    Article  MathSciNet  Google Scholar 

  10. A. Connes, H.Narnhofer and W. Thirrng, Dynamical entropy of C*-algebras and von Neumann algebrasCommun. Math. Phys. 112, 691–719 (1987).

    Article  ADS  MATH  Google Scholar 

  11. F.Goodman, P.de la Harpe and V. Jones, Coxter graphs and towers of algebras, (Springer, 1989).

    Google Scholar 

  12. U. Haagerup: in preparation.

    Google Scholar 

  13. M. Izumi: Application of fusion rules to classification of subfactors, Publ., RIMS, Kyoto Univ., 24, 953–994 (1988).

    Google Scholar 

  14. M. Izumi and Y. Kawahigashi: Classification of subfactors with the principal graph D n (1) Preprint.

    Google Scholar 

  15. M. Izumi: On flatness of the Coxeter graph E 8 Preprint.

    Google Scholar 

  16. V. F. R. Jones, Index for subfactors, Invent. Math., 72, 1–25 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Y. Kawahigashi: On flatness of Ocneanu’s connections on the Dynkyn diagrams and classification of subfactors, Preprint.

    Google Scholar 

  18. Y. Kawahigashi: Exactly solvable orbifold models and subfactors, to appear in Functional analysis conference at Kyoto, (1991).

    Google Scholar 

  19. R. Longo, Simple injective subfactors, Adv. in Math.,63 152–171 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Longo: Index of subfactors and statistics of quantum fields I, Commun. Math. Phys., 126 217–247 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. R. Longo: Index of subfactors and statistics of quantum fields II, Commun. Math. Phys., 130 285–309(1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. A. Ocneanu: Quantized groups, string algebras and Galois theory, Preprint. Quantized groups, string algebras and Galios theory in Operator algebras and applications, vol. II, Cambridge Univ. Press, (1988).

    Google Scholar 

  23. A. Ocneanu: Quantum symmetry, differential geometry of finite graphs and classification of subfactors, Notes by Kawahigashi.

    Google Scholar 

  24. S. Okamoto: Invariants for subfactors arizing from Coxeter graphs, Current topics in Operator algebras, World Scientific, (1991).

    Google Scholar 

  25. M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. Ec. Norm. Sup., 19, 57–106 (1986).

    MathSciNet  MATH  Google Scholar 

  26. M. Pimsner and S. Popa, Iterating the basic construction, Trans. A. M. S.,310 127–134(1988).

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Popa, Maximal injective subalgebras iin factors associated with free groups, Adv. In Math., 50, 27–48(1983).

    Article  MathSciNet  MATH  Google Scholar 

  28. S. Popa, Classification of subfactors: the Reduction to commuting squares, Invent. Math.,101 19–43(1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. S. Popa, Sur classification des sousfacteurs d’indice fini du facteur hyperfini, C. R. Acad. Sc. Paris, 311, 95–100(1990).

    MATH  Google Scholar 

  30. S. Popa, Classification of amenable subfactors of type III, Preprint.

    Google Scholar 

  31. R. T. Powers, An index theory for semigroups of *;-endomorphisms of B(H) and type II1 factors, Canad. J. Math., 40, 86–114 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  32. A. J. Wassermann, Coaction and Yang-Baxter equations for ergodic actions and subfactors, Operator algebras and applications, Cambridge Univ. Press, II, (1988).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of mathematics, Osaka Kyoiku University, Tennoji, Osaka, 543, Japan

    Marie Choda

Authors
  1. Marie Choda
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Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Sakyo-ku, Kyoto, Japan

    Huzihiro Araki

  2. Department of Mathematics and Information, College of Liberal Arts, Kyoto University, Sakyo-ku, Yoshida Kyoto 606, Japan

    Keiichi R. Ito

  3. Department of Mathematics Faculty of Science, Hokkaido University, Sapporo 060, Japan

    Akitaka Kishimoto

  4. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Kyoto, Japan

    Izumi Ojima

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© 1993 Springer Science+Business Media Dordrecht

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Choda, M. (1993). Endomorphisms and Automorphisms for Factor Inclusions. In: Araki, H., Ito, K.R., Kishimoto, A., Ojima, I. (eds) Quantum and Non-Commutative Analysis. Mathematical Physics Studies, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2823-2_22

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  • DOI: https://doi.org/10.1007/978-94-017-2823-2_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4334-4

  • Online ISBN: 978-94-017-2823-2

  • eBook Packages: Springer Book Archive

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