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

David Robertson; Wojciech Szymański

$C^$-algebras associated to $C^$-correspondences and applications to mirror quantum spheres

Operator Algebras 2010-12-15 v2

Authors: David Robertson , Wojciech Szymański

Abstract

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.

Keywords

c*-algebras c*-correspondences cuntz-pimsner algebras labelled graphs mirror quantum spheres functor

Cite

@article{arxiv.1001.2982,
  title  = {$C^*$-algebras associated to $C^*$-correspondences and applications to mirror quantum spheres},
  author = {David Robertson and Wojciech Szymański},
  journal= {arXiv preprint arXiv:1001.2982},
  year   = {2010}
}

Comments

27 pages