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.Comment: 27 page