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.
Full Text
Article Information
| Title | On isometries satisfying deformed commutation relations |
| Source | Methods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 152-160 |
| MathSciNet |
MR3978679 |
| Milestones | Received 02/04/2019 |
| Copyright | The 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
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},
MRNUMBER = {MR3978679},
URL = {http://mfat.imath.kiev.ua/article/?id=1170},
}
