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Operator Algebras and Abstract Duals: Progress and Problems

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Quantum and Non-Commutative Analysis

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

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Mount Fuji and the Ocean are immune to aging; so may Huzihiro long continue being volcanic and deep.

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References

  1. E. Hewitt, K.A. Ross, Abstract harmonic analysis II, Springer-Verlag, New York (1970).

    Google Scholar 

  2. S. Doplicher, J.E. Roberts, Fields, statistics and non-abelian gauge groups, Commun. Math. Phys., 28, 331–348 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Doplicher, R. Haag, J.E. Roberts, Local observables and particle statistics I, Commun. Math. Phys., 23, 199–230 (1971); II, Commun. Math. Phys., 35, 49–95 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  4. S. Doplicher, J.E. Roberts, Endomorphisms of C’—algebras, cross products and duality for compact groups, Ann. Math., 130, 75–119 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Doplicher, J.E. Roberts, A new duality theory for compact groups, Inventions Math., 89, 157–218 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  6. S. Doplicher, Abstract compact group duals, operator algebras and Quantum Field Theory, Proceedings of the ICM-90, Kyoto; Springer, 1991.

    Google Scholar 

  7. J. Cuntz, Simple C`—algebras generated by isometries, Commun. Math. Phys., 57, 173–185 (1977).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. D. Buchholz, S. Doplicher, R. Longo, J.E. Roberts, Extension of Automorphisms and Gauge symmetries, Commun. Math. Phys.,to appear.

    Google Scholar 

  9. S. Doplicher, J.E. Roberts, Compact group actions on Cs—algebras, Jours. Operator Theory, 19, 293–305 (1988).

    MathSciNet  Google Scholar 

  10. P. Deligne, Categories tannakiennes, Grothendieck Festschrift, Birkhäuser (1990).

    Google Scholar 

  11. S. Doplicher, J.E. Roberts, Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys., 131, 51–107 (1990).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  12. D. Buchholz, K. Fredenhagen, Locality and the structure of particle states, Commun. Math. Phys., 84, 1–54 (1982).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. D. Buchholz, S. Doplicher, R. Longo, J.E. Roberts, A new look at Goldstone’s Theorem, Reviews in Mathematical Physics, to appear.

    Google Scholar 

  14. D. Handelman, Representation rings as invariants for compact groups and limit ratio Theorems for them, University of Ottawa preprint, 1991.

    Google Scholar 

  15. M. Takesaki, A characterization of group algebras as a converse of TannakaStinespring—Tatsuuma duality Theorem, American Journ. Math., 91, 529–564 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  16. S.L. Woronowicz, Tannaka—Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Inventiones Math., 93, 35–76 (1988).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. D. Yetter, Math. Proceedings Came. Phil. Soc., 108, 261–290 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Baaj, G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croises de C’—algebres, preprint.

    Google Scholar 

  19. K. Fredenhagen, K.H. Rehren, B. Schroer, Superselection sectors with braid group statistics and exchange algebras I, Commun. Math. Phys.,125, 201–226 (1989); II preprint.

    Google Scholar 

  20. A. Joyal, R. Street, Braided monoidal categories, Mcquarie Mathematics Reports n. 860081 (1986).

    Google Scholar 

  21. T. Ceccherini, S. Doplicher, C. Pinzari, J.E. Roberts, A generalization of the Cuntz Algebras and Model Actions, preprint.

    Google Scholar 

  22. S. Doplicher, Operator algebra and group duality in Current topics in operator algebras, H. Araki, H. Choda, Y. Nakagami, K. Saitô and J. Tomiyama editors, World Scientific, 1991.

    Google Scholar 

  23. S. Doplicher, Operator Algebras, group actions and abstract duals, to appear in the proceedings of the Istambul conference on Operator Algebras, 1991.

    Google Scholar 

  24. J. Cuntz, Regular actions of Hopf algebras on the C’—algebra generated by a Hilbert space, preprint.

    Google Scholar 

  25. S. Doplicher, J.E. Roberts, Duals of compact Lie groups realized in the Cuntz algebras and their action on C’—algebras, Journ. Functional Analysis, 73, 96–120 (1987).

    Article  MathSciNet  Google Scholar 

  26. T. Ceccherini, C. Pinzari, Canonical actions on 0,,,,„ Journ. Functional Analysis, 103, 26–39 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Pinzari, Semigroups of non—urvital endomorphisms of C’—algebras and compact group duality, Journ. Functional Analysis,(to appear).

    Google Scholar 

  28. N. Tatsuuma, A duality Theorem for locally compact groups, J. Math. Kyoto University, 6, 197–293 (1967).

    MathSciNet  Google Scholar 

  29. R. Longo, A duality for Hopf algebras and for subfactors I, preprint.

    Google Scholar 

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Dedicated to Professor Huzihiro Araki on the occasion of his “Kanreki”.

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© 1993 Springer Science+Business Media Dordrecht

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Doplicher, S. (1993). Operator Algebras and Abstract Duals: Progress and Problems. 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_32

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  • DOI: https://doi.org/10.1007/978-94-017-2823-2_32

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4334-4

  • Online ISBN: 978-94-017-2823-2

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