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SIGMA, 2012, Volume 8, 091, 12 pages (Mi sigma768)  

This article is cited in 1 scientific paper (total in 1 paper)

Covariant Fields of $C^*$-Algebras under Rieffel Deformation

Fabian Belmontea, Marius Măntoiub

a 728, building A, SISSA-ISAS, Via Bonomea 265, 34136 Trieste, Italy
b Departamento de Matemáticas, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile

Abstract: We show that Rieffel's deformation sends covariant $\mathcal{C}(T)$-algebras into $\mathcal{C}(T)$-algebras. We also treat the lower semi-continuity issue, proving that Rieffel's deformation transforms covariant continuous fields of $C^*$-algebras into continuous fields of $C^*$-algebras. Some examples are indicated, including certain quantum groups.

Keywords: pseudodifferential operator; Rieffel deformation; $C^*$-algebra; continuous field; noncommutative dynamical system

DOI: https://doi.org/10.3842/SIGMA.2012.091

Full text: PDF file (397 kB)
Full text: http://emis.mi.ras.ru/.../091
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Bibliographic databases:

ArXiv: 1101.2751
MSC: 35S05; 81Q10; 46L55; 47C15
Received: August 26, 2012; in final form November 22, 2012; Published online November 28, 2012
Language:

Citation: Fabian Belmonte, Marius Măntoiu, “Covariant Fields of $C^*$-Algebras under Rieffel Deformation”, SIGMA, 8 (2012), 091, 12 pp.

Citation in format AMSBIB
\Bibitem{BelMan12}
\by Fabian~Belmonte, Marius~M{\u a}ntoiu
\paper Covariant Fields of $C^*$-Algebras under Rieffel Deformation
\jour SIGMA
\yr 2012
\vol 8
\papernumber 091
\totalpages 12
\mathnet{http://mi.mathnet.ru/sigma768}
\crossref{https://doi.org/10.3842/SIGMA.2012.091}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007268}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312436100001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870338397}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. van Suijlekom W.D., “Localizing Gauge Theories From Noncommutative Geometry”, Adv. Math., 290 (2016), 682–708  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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