Journal article
On C-algebras generated by pairs of q-commuting isometries
Journal of physics. A, Mathematical and general, Vol.38(12), pp.2669-2680
11/07/2003
DOI: 10.1088/0305-4470/38/12/009
Abstract
J. Phys. A: Math. Gen. 38 (2005) 2669-2680 We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.
Details
- Title: Subtitle
- On C-algebras generated by pairs of q-commuting isometries
- Creators
- Palle E. T Jorgensen - University of IowaDaniil P Proskurin - Kyiv Taras Shevchenko UniversityYurii S Samoilenko - Institute of Mathematics, National Academy of Sciences of Ukraine
- Resource Type
- Journal article
- Publication Details
- Journal of physics. A, Mathematical and general, Vol.38(12), pp.2669-2680
- DOI
- 10.1088/0305-4470/38/12/009
- ISSN
- 0305-4470
- eISSN
- 1361-6447
- Language
- English
- Date published
- 11/07/2003
- Academic Unit
- Mathematics
- Record Identifier
- 9983985912402771
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