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On C*-Algebras Generated by Deformations of CCR

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Abstract

We consider C*-algebras generated by deformations of classical commutation relations (CCR), which are generalizations of commutation relations for generalized quons and twisted CCR. We show that the Fock representation is a universal bounded representation. We discuss the connection between the presented deformations and extensions of many-dimensional noncommutative tori.

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REFERENCES

  1. M. Bozejko and R. Speicher, “An example of a generalized Brownian motion,” Commun. Math. Phys., 137, 519–531 (1991).

    Google Scholar 

  2. M. Bozejko and R. Speicher, “Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces,” Math. Ann., 300, 97–120 (1994).

    Article  Google Scholar 

  3. W. Marcinek, “On commutation relations for quons,” Repts Math. Phys., 41, 155–172 (1998).

    Article  Google Scholar 

  4. V. L. Ostrovsky and D. P. Proskurin, “Operator relations, dynamical systems, and representations of a class of Wick algebras,” Oper. Theor. Adv. Appl., 118, 335–345 (2000).

    Google Scholar 

  5. W. Pusz and S. L. Woronowicz, “Twisted second quantization,” Repts Math. Phys., 27, 251–263 (1989).

    Google Scholar 

  6. L. Vaksman, Lectures on q-Analogues of Cartan Domains and Associated Harish-Chandra Modules, Math. QA/0109198.

  7. D. Proskurin, “Stability of a special class of q ij -CCR and extensions of higher-dimensional noncommutative tori,” Lett. Math. Phys., 52, No.2, 165–175 (2000).

    Article  Google Scholar 

  8. P. E. T. Jorgensen, L. M. Schmitt, and R. F. Werner, “q-Canonical commutation relations and stability of the Cuntz algebra,” Pacif. J. Math., 163, No.1, 131–151 (1994).

    Google Scholar 

  9. D. Proskurin and Yu. Samoilenko, “Stability of the C*-algebra associated with the twisted CCR,” Algebras Rept. Theor., 5, 433–444 (2002).

    Article  Google Scholar 

  10. Z. Kabluchko, “On the existence of the higher-dimensional noncommutative tori,” Meth. Func. Anal. Top., 1, 28–33 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Gottingen University, Gottingen, Germany

    Z. A. Kabluchko

  2. Shevchenko Kiev National University, Kiev, Ukraine

    D. P. Proskurin

  3. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    Yu. S. Samoilenko

Authors
  1. Z. A. Kabluchko
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  2. D. P. Proskurin
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  3. Yu. S. Samoilenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1527–1538, November, 2004.

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Kabluchko, Z.A., Proskurin, D.P. & Samoilenko, Y.S. On C*-Algebras Generated by Deformations of CCR. Ukr Math J 56, 1813–1827 (2004). https://doi.org/10.1007/s11253-005-0153-3

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  • DOI: https://doi.org/10.1007/s11253-005-0153-3

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