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The smallestC*-algebra for canonical commutations relations

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Abstract

We consider theC*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a universalC*-algebra by some of its ideals, and we characterize all these ideals.

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References

  1. Slawny J.: On factor representations and the C*-algebra of canonical communications relations. Preprint (1971).

  2. Manuceau, J.: Ann. Inst. Henri PoincaréVIII (2), 139 (1968).

    Google Scholar 

  3. Rocca, F., Sirugue, M., Testard, D.: Commun. math. Phys.19, 119 (1970).

    Google Scholar 

  4. Grossmann, A.: Private communications.

  5. Naimark, M. A.: Normed rings. Groningen, The Netherlands: 1966. P. Noordhoff N. W.

    Google Scholar 

  6. Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien. Paris: 1969. Gauthier-Villars.

    Google Scholar 

  7. Doplicher, S., Kastler, D., Stormer, E.: J. of Functional Analysis3 (3), 419 (1969).

    Google Scholar 

  8. Stormer, E.: Asymptotically Abelian systems. Cargèse Lectures in Physics (Vol. 4). New York: 1969. Gordon and Breach.

    Google Scholar 

  9. Takesaki, M.: Tomita's theory of modular Hilbert algebras and its applications. Berlin-Heidelberg-New York: Springer 1970.

    Google Scholar 

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Authors and Affiliations

  1. Centre de Physique Théorique, C.N.R.S., Marseille, France

    J. Manuceau, M. Sirugue, D. Testard & A. Verbeure

  2. Université de Provence, F-13274, Marseille, France

    J. Manuceau

  3. Centre Universitaire d'Avignon, Avignon, France

    D. Testard

  4. Dept. Natuurkunde, Instituut voor Theoretische Natuurkunde, Celestijnenlaan 200 D, B-3030, Heverlee, (Leuven), Belgium

    A. Verbeure

Authors
  1. J. Manuceau
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  2. M. Sirugue
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  3. D. Testard
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  4. A. Verbeure
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Manuceau, J., Sirugue, M., Testard, D. et al. The smallestC*-algebra for canonical commutations relations. Commun.Math. Phys. 32, 231–243 (1973). https://doi.org/10.1007/BF01645594

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  • DOI: https://doi.org/10.1007/BF01645594

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