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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ C^*$-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras


Author: B. K. Kwaśniewski
Journal: Trans. Amer. Math. Soc. 365 (2013), 1809-1873
MSC (2010): Primary 46L08, 46M99
Published electronically: December 13, 2012
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Abstract: We introduce and analyse the structure of $ C^*$-algebras arising from ideals in right tensor $ C^*$-precategories, which naturally unify the approaches based on Hilbert $ C^*$-modules and $ C^*$-categories with tensor structure. We establish an explicit intrinsic construction of the algebras considered, prove a number of key results such as a structure theorem and a gauge-invariant uniqueness theorem, and describe the gauge-invariant ideal structure. These results give a new insight into the corresponding statements for relative Cuntz-Pimsner algebras and are applied to Doplicher-Roberts algebras associated with $ C^*$-correspondences.


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Additional Information

B. K. Kwaśniewski
Affiliation: Institute of Mathematics, University of Bialystok, ul. Akademicka 2, PL-15-267 Bialystok, Poland
Email: bartoszk@math.uwb.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05748-5
PII: S 0002-9947(2012)05748-5
Keywords: Relative Cuntz-Pimsner algebra, Doplicher-Roberts algebra, right tensor $C^{*}$-precategory
Received by editor(s): March 24, 2011
Published electronically: December 13, 2012
Additional Notes: The author would like to thank the referee whose comments helped improve the text significantly in several places. This work was supported in part by Polish Ministry of Science and High Education grant number N N201 382634 and Polish National Science Centre grant number DEC-2011/01/D/ST1/04112
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.