CCR and CAR Algebras are Connected Via a Path of Cuntz–Toeplitz Algebras

Journal article, 2023

For q∈ R, | q| < 1 we consider the universal enveloping C∗-algebra of a ∗ -algebra of q-canonical commutation relations (q-CCR), which is generated by a1, … , an subject to the relations ai∗aj=δij1+qajai∗.It has a distinguished representation πF called the Fock representation, which is believed to be faithful. In this article we denote the image of the universal enveloping C∗-algebra of q-CCR in the Fock representation by ℶn,q. The question whether C∗-isomorphism ℶn,q≃ ℶn, holds has been considered in the literature and proved for | q| < 0.44. In this article we show that ℶn,q≃ ℶn, for | q| < 1.