C*-algebras associated to C*-correspondences and applications to mirror quantum spheres

The structure of the C*-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain C*-correspondences and C*-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and C*-correspondences are studied. A functor from labelled graphs to C*-correspondences is constructed, such that the corresponding associated C*-algebras are isomorphic. Furthermore, it is shown that C*-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.