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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cuntz-Pimnser algebras, completely positive maps and Morita equivalence


Authors: Alberto E. Marrero and Paul S. Muhly
Journal: Proc. Amer. Math. Soc. 134 (2006), 1133-1135
MSC (2000): Primary 46L07, 46L08, 46M18, 47L30
Published electronically: August 12, 2005
MathSciNet review: 2196048
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Abstract: Let $P$ be a completely positive map on $M_n(\mathbb{C} )$ and let $E_P$ be the associated 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 $P$.


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Additional Information

Alberto E. Marrero
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication: Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana 46383-6493
Email: amarrero@math.uiowa.edu

Paul S. Muhly
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: pmuhly@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08110-4
PII: S 0002-9939(05)08110-4
Keywords: Cuntz-Pimsner algebras, completely positive maps, Morita equivalence
Received by editor(s): November 2, 2004
Published electronically: August 12, 2005
Additional Notes: The research of the authors was supported in part by a grant from the National Science Foundation, DMS-0070405. The first author was also supported by a GAANN Fellowship and the Sloan Foundation.
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.