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

Abstract

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