$C^{\ast }$-algebras associated to $C^{\ast }$-correspondences and applications to mirror quantum spheres

Abstract

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

27 pages

References in corpus (4)

• Adding tails to C*-correspondences
• Computing K-theory and Ext for graph C*-algebras
• C*-algebras of labelled graphs
• Noncommutative Balls and Mirror Quantum Spheres