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On isometries satisfying deformed commutation relations


Abstract

We consider an $C^*$-algebra $\mathcal{E}_{1,n}^q$, $q\le 1$, generated by isometries satisfying $q$-deformed commutation relations. For the case $|q|<1$, we prove that $\mathcal E_{1,n}^q \simeq\mathcal E_{1,n}^0=\mathcal O_{n+1}^0$. For $|q|=1$ we show that $\mathcal E_{1,n}^q$ is nuclear and prove that its Fock representation is faithul. In this case we also discuss the representation theory, in particular construct a commutative model for representations.

Key words: Cuntz-Toeplitz algebra, $q$-deformation, Fock representation, commutative model.


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Article Information

TitleOn isometries satisfying deformed commutation relations
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 152-160
MilestonesReceived 02/04/2019
CopyrightThe Author(s) 2019 (CC BY-SA)

Authors Information

Olha Ostrovska
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Roman Yakymiv
Faculty of Computer Sciences and Cybernetics, Kiev National Taras Shevchenko University


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Citation Example

Olha Ostrovska and Roman Yakymiv, On isometries satisfying deformed commutation relations, Methods Funct. Anal. Topology 25 (2019), no. 2, 152-160.


BibTex

@article {MFAT1170,
    AUTHOR = {Olha Ostrovska and Roman Yakymiv},
     TITLE = {On isometries satisfying deformed commutation relations},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {25},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {152-160},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1170},
}


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