Ukrainian Mathematical Journal

, Volume 56, Issue 11, pp 1813–1827 | Cite as

On C*-Algebras Generated by Deformations of CCR

  • Z. A. Kabluchko
  • D. P. Proskurin
  • Yu. S. Samoilenko


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.


Commutation Relation Bounded Representation Algebra Generate Noncommutative Tori Classical Commutation 
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  1. 1.
    M. Bozejko and R. Speicher, “An example of a generalized Brownian motion,” Commun. Math. Phys., 137, 519–531 (1991).Google Scholar
  2. 2.
    M. Bozejko and R. Speicher, “Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces,” Math. Ann., 300, 97–120 (1994).CrossRefGoogle Scholar
  3. 3.
    W. Marcinek, “On commutation relations for quons,” Repts Math. Phys., 41, 155–172 (1998).CrossRefGoogle Scholar
  4. 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. 5.
    W. Pusz and S. L. Woronowicz, “Twisted second quantization,” Repts Math. Phys., 27, 251–263 (1989).Google Scholar
  6. 6.
    L. Vaksman, Lectures on q-Analogues of Cartan Domains and Associated Harish-Chandra Modules, Math. QA/0109198.Google Scholar
  7. 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).CrossRefGoogle Scholar
  8. 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. 9.
    D. Proskurin and Yu. Samoilenko, “Stability of the C*-algebra associated with the twisted CCR,” Algebras Rept. Theor., 5, 433–444 (2002).CrossRefGoogle Scholar
  10. 10.
    Z. Kabluchko, “On the existence of the higher-dimensional noncommutative tori,” Meth. Func. Anal. Top., 1, 28–33 (2001).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Z. A. Kabluchko
    • 1
  • D. P. Proskurin
    • 2
  • Yu. S. Samoilenko
    • 3
  1. 1.Gottingen UniversityGottingenGermany
  2. 2.Shevchenko Kiev National UniversityKievUkraine
  3. 3.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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