Ukrainian Mathematical Journal

, Volume 62, Issue 2, pp 227–240 | Cite as

On ∗-representations of deformations of canonical anticommutation relations

  • D. P. Proskurin
  • K. M. Sukretnyi

We consider irreducible ∗-representations of deformations of canonical anticommutation relations (CAR) that belong to the class of ∗-algebras generated by generalized quons.


Irreducible Representation Unitary Operator Direct Summand Partial Isometry Canonical Commutation Relation 
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  1. 1.
    W. Marcinek, “On commutation relations for quons,” Rep. Math. Phys., 41, No. 2, 155–172 (1998).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    W. Marcinek and R. Ralowski, “On Wick algebras with braid relations,” J. Math. Phys., 36, No. 6, 2803–2812 (1995).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    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).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    V. Ostrovskyi and Yu. Samoilenko, Introduction to the Theory of Representations of Finitely Presented-Algebras, I: Representations by Bounded Operators, Gordon and Breach, London (1999).Google Scholar
  5. 5.
    D. Proskurin, Yu. Savchuk, and L. Turowska, “On C -algebras generated by some deformations of CAR relations,” in: Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics, Vol. 391, American Mathematical Society, Providence, RI (2005), pp. 297–312.Google Scholar
  6. 6.
    S. Albeverio, D. Proskurin, and L. Turowska, “On ∗-representations of a deformation of a Wick analogue of the CAR algebra,” Rep. Math. Phys., 56, No. 2, 175–196 (2005).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Z. L. Kabluchko, D. P. Proskurin, and Yu. S. Samoilenko, “On C -algebras generated by deformations of CCR,” Ukr. Math. J., 56, No. 11, 1813–1827 (2004).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • D. P. Proskurin
    • 1
  • K. M. Sukretnyi
    • 2
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine
  2. 2.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine

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