On $q$-tensor product of Cuntz algebras

Abstract

We consider $C^{\ast }$-algebra ${\mathcal{E}}_{n,m}^q$, 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, thus showing that the isomorphism class of ${\mathcal{E}}_{n,m}^q$ does not depend of $q$. For the case $|q|=1$ we give an explicit description of all ideals in ${\mathcal{E}}_{n,m}^q$. In particular ${\mathcal{E}}_{n,m}^q$ contains unique largest ideal ${\mathcal{M}}_q$. Then we identify ${\mathcal{E}}_{n,m}^q/{\mathcal{M}}_q$ with the Rieffel deformation of ${\mathcal{O}}_n\otimes {\mathcal{O}}_m$ and use a K-theoretical argument to show that the isomorphism class does not depend on $q$.

48 pages

References in corpus (2)

• Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
• On C*-algebras generated by pairs of q-commuting isometries