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Vector Bundles and Bimodules

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Quantum and Non-Commutative Analysis

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

Abstract

A vector bundle construction for bimodules is discussed with an application to finite dimensional Kac algebras.

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References

  1. S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C*-algébres:deux nouveaux appendices, preprint.

    Google Scholar 

  2. F. M. Goodman, P. de la Harpe, and V. Jones, Coxeter-Dynkin Diagrams and Towers of Algebras, Springer, (1989).

    Google Scholar 

  3. J. F. Havet, Espérance conditionnelle minimale, J. Operator Theory, 24 (1990), 3355.

    MathSciNet  Google Scholar 

  4. F. Hiai, Minimizing indices of conditional expectations onto a subfactor, Publ. RIMS, Kyoto Univ, 24 (1988), 673–678.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Kosaki, Canonical LP-spaces associated with an arbitrary abstract von Neumann algebra, Thesis at UCLA, (1980).

    Google Scholar 

  6. H. Kosaki, Extension of Jones’ theory on index to arbitrary factors, J. Funct. Anal., 66 (1986), 123–140.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Kosaki and R. Longo, A remark on the minimal index of subfactors, J. Funct. Analysis, 107 (1992), 458–470.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Kosaki and S. Yamagami, Irreducible bimodules associated with crossed product algebras, to appear in International. J. Math.

    Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. R. Longo, Minimal index and braided subfactors, preprint.

    Google Scholar 

  11. S. Majid, Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra, 130 (1990), 17–64.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Ocneanu, Quantized groups, string algebras, and Galois theory for algebras, Operator algebras and applications, vol. 2, Warwick(1987), Cambridge University Press, (1988).

    Google Scholar 

  13. A. Ocneanu, Quantum Symmetry, Differential Geometry of Finite Graphs and Classi- fication of Subfactors, University of Tokyo Seminary Notes, (1991).

    Google Scholar 

  14. J.-L. Sauvageot, Sur le prodiut tensoriel relatif d’espaces de hilbert, J. Operator Theory, 9 (1983), 237–252.

    MathSciNet  MATH  Google Scholar 

  15. W. Szymanski, Finite index subfactors and Hopf algebra crossed products, preprint.

    Google Scholar 

  16. Yamagami S., Algebraic aspects in modular theory, to appear in Publ. RIMS.

    Google Scholar 

  17. Yamagami S., Modular theory for bimodules, preprint(1992).

    Google Scholar 

  18. Yamagami S., A note on Ocneanu’s approach to Jones’ index theory, preprint(1992).

    Google Scholar 

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© 1993 Springer Science+Business Media Dordrecht

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Shigeru, Y. (1993). Vector Bundles and Bimodules. 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_25

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  • DOI: https://doi.org/10.1007/978-94-017-2823-2_25

  • 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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