On stability of deformations of Cuntz – Toeplitz algebras
Abstract
UDC 517.986.2
We study $C^*$-algebras $\mathcal{O}_{n+m}^{\hat{q}}$ generated by isometries $\{s_i\}_{i=1}^n\cup\{t_j\}_{j=1}^m,$ where isometries from the same collection are orthogonal and isometries from different collections are $q_{i,j}$-commuting.
It is shown that if $|q_{i,j}|<1,$ then $C^*$-algebra $\mathcal{O}_{n+m}^{\hat{q}}$ is isomorphic to Cuntz -Toeplitz algebra $\mathcal{O}_{n+m}^{0}.$
References
P. E. T. Jorgensen, L. M. Schmitt, R. F. Werner, Positive representations of general commutation relations allowing Wick ordering, J. Funct. Anal., 134, № 1, 33 – 99 (1995), https://doi.org/10.1006/jfan.1995.1139 DOI: https://doi.org/10.1006/jfan.1995.1139
P. E. T. Jorgensen, L. M. Schmitt, R. F. Werner, $q$-Canonical commutation relations and stability of the Cuntz algebra, Pacif. J. Math., 165, № 1, 131 – 151 (1994). DOI: https://doi.org/10.2140/pjm.1994.165.131
P. E. T. Jorgensen, D. P. Proskurin, Y. S. Samoilenko, On $C^{ast}$ -algebras generated by pairs of $q$-commuting isometries, J. Phys. A, 38, № 12, 2669 – 2680 (2005), https://doi.org/10.1088/0305-4470/38/12/009 DOI: https://doi.org/10.1088/0305-4470/38/12/009
A. Kuzmin, V. Ostrovskyi, D. Proskurin, R. Yakymiv, On $q$-tensor product of Cuntz algebras, Preprint (2019).
A. Kuzmin, N. Pochekai, Faithfulness of the Fock representation of the $C^*$ -algebra generated by $q_{ij}$ -commuting isometries, J. Operator Theory, 80, № 1, 77 – 93 (2018), https://doi.org/10.7900/jot.2017jun01.2172 DOI: https://doi.org/10.7900/jot.2017jun01.2172
K. Dykema, A. Nica, On the Fock representation of the $q$-commutation relations, J. reine and angew. Math., 440, 201 – 212 (1993) DOI: https://doi.org/10.1515/crll.1993.440.201
Copyright (c) 2021 Kostyantyn Krutoy
This work is licensed under a Creative Commons Attribution 4.0 International License.
