2003/11/13 by Palle E. T. Jørgensen, Palle E. T. Jorgensen, Daniil Proskurin +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory #math.OA
paper · pdf · doi:10.1088/0305-4470/38/12/009
published as J. Phys. A: Math. Gen. 38 (2005) 2669-2680 · 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treated
arxiv created 2003/11/13 · openalex publication_date 2005/03/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider the C*-algebras O2q and A2q generated, respectively, by isometries s1, s2 satisfying the relation s1^* s2 = q s2 s1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s1, s2 satisfying the relation s2 s1 = q s1 s2 with |q| = 1. We show that O2q is isomorphic to the Cuntz-Toeplitz C*-algebra O20 for any |q| < 1. We further prove that A2q1 is isomorphic to A2q2 if and only if either q1 = q2 or q1 = complex conjugate of q2. In the second part of our paper, we discuss the complexity of the representation theory of A2q. We show that A2q is *-wild for any q in the circle |q| = 1, and hence that A2q is not nuclear for any q in the circle.