Cuntz-Pimnser algebras, completely positive maps and Morita equivalence
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- by Alberto E. Marrero and Paul S. Muhly PDF
- Proc. Amer. Math. Soc. 134 (2006), 1133-1135 Request permission
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 $P$.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1133-1135
- MSC (2000): Primary 46L07, 46L08, 46M18, 47L30
- DOI: https://doi.org/10.1090/S0002-9939-05-08110-4
- MathSciNet review: 2196048