On C*-algebras generated by pairs of q-commuting isometries
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.
Keywords
Cite
@article{arxiv.math/0311115,
title = {On C*-algebras generated by pairs of q-commuting isometries},
author = {Palle E. T. Jorgensen and Daniil P. Proskurin and Yurii S. Samoilenko},
journal= {arXiv preprint arXiv:math/0311115},
year = {2007}
}
Comments
18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treated