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On C*-algebras generated by pairs of q-commuting isometries

Palle E. T. Jorgensen·Daniil P. Proskurin·Yurii S. Samoilenko
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Abstract

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.

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Palle E. T. Jorgensen, Daniil P. Proskurin, Yurii S. Samoilenko. 2003-11-13. On C*-algebras generated by pairs of q-commuting isometries. https://doi.org/10.1088/0305-4470/38/12/009

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