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Equivalence of commutation relations

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Abstract

We consider C*-algebras of commutation relations over the fields p, p = 2, 3, 5, …, ∞. We describe all the irreducible separable representations of these algebras. We prove that the algebras are not isomorphic at different p.

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References

  1. 1.

    G. W. Mackey, Duke Math. J., 16, 311–326 (1949).

  2. 2.

    M. Rieffel, Duke Math. J., 39, 745–752 (1972).

  3. 3.

    G. J. Murphy, C*-Algebras and Operator Theory, Acad. Press, Boston, Mass. (1990).

  4. 4.

    E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Structure of Topological Groups, Integration Theory, Group Representations (Grundlehren Math. Wiss., Vol. 115), Springer, New York (1979); Abstract Harmonic Analysis, Vol. 2, Structure and Analysis for Compact Groups, Analysis on Locally Compact Abelian Groups (Grundlehren Math. Wiss., Vol. 152), Springer, New York (1970).

  5. 5.

    V. S. Vladimirov, I. V. Volovich, and Ye. I. Zelenov, p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994); English transl. (Ser. Sov. East Eur. Math., Vol. 1), World Scientific, Singapore (1994).

  6. 6.

    J. Slawny, Comm. Math. Phys., 24, 151–170 (1972).

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Additional information

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 406–412, December, 2008.

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Zelenov, E.I. Equivalence of commutation relations. Theor Math Phys 157, 1707–1712 (2008). https://doi.org/10.1007/s11232-008-0142-4

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Keywords

  • commutation relation
  • p-adic topology
  • irreducible representation
  • equivalence of representations