On stability of deformations of Cuntz – Toeplitz algebras
DOI:
https://doi.org/10.37863/umzh.v73i5.6590Keywords:
C*-algebras, Cuntz-Toeplitz algebra, algebras allowing Wick orderingAbstract
UDC 517.986.2
We study C∗-algebras Oˆqn+m generated by isometries {si}ni=1∪{tj}mj=1, where isometries from the same collection are orthogonal and isometries from different collections are qi,j-commuting.
It is shown that if |qi,j|<1, then C∗-algebra Oˆqn+m is isomorphic to Cuntz -Toeplitz algebra O0n+m.
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 Cast -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 qij -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
