Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence

Alberto E. Marrero; Paul S. Muhly

Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence

Operator Algebras 2007-05-23 v1 Mathematical Physics math.MP

Authors: Alberto E. Marrero , Paul S. Muhly

Abstract

Let $P$ be a completely positive map on $M_n(\mathbb{C})$ and let $E_P$ be the associated \emph{GNS}- $C^*$ -correspondence. We prove a result that implies, in particular, that the Cuntz-Pimsner algebra of $E_P$ , $\mathcal{O}(E_P)$ , is strongly Morita equivalent to the Cuntz algebra $\mathcal{O}_{d(P)}$ , where $d(P)$ is the index of $P$ .

Keywords

cuntz-pimsner algebras completely positive maps morita equivalence gns-c*-correspondence cuntz algebras

Cite

@article{arxiv.math/0409511,
  title  = {Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence},
  author = {Alberto E. Marrero and Paul S. Muhly},
  journal= {arXiv preprint arXiv:math/0409511},
  year   = {2007}
}

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