C~*-ALGEBRAS ASSOCIATED TO C~*-CORRESPONDENCES AND APPLICATIONS TO MIRROR QUANTUM SPHERES

摘要

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.