On q-tensor products of Cuntz algebras

Journal article, 2022

We consider the C∗-algebra Eqn, m, which is a q-twist of two Cuntz-Toeplitz algebras. For the case |q| < 1, we give an explicit formula which untwists the q-deformation showing that the isomorphism class of Eqn, mdoes not depend on q. For the case |q| = 1, we give an explicit description of all ideals in Eqn, m. In particular, we show that Eqn, mcontains a unique largest ideal Mq. We identify Eqn, m/Mq with the Rieffel deformation of On ⊗Om and use a K-theoretical argument to show that the isomorphism class does not depend on q. The latter result holds true in a more general setting of multiparameter deformations.