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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 075, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.075 (Mi sigma1056) 		 
This article is cited in 26 scientific papers (total in 26 papers)

An Asymmetric Noncommutative Torus

Ludwik Dąbrowskia, Andrzej Sitarzbc

a SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136 Trieste, Italy
b Institute of Physics, Jagiellonian University, Stanisława Lojasiewicza 11, 30-348 Kraków, Poland
c Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
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DOI: https://doi.org/10.3842/SIGMA.2015.075
Abstract: We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar curvature and show that the Gauss–Bonnet theorem holds (which is not covered by the general result of Connes and Moscovici).
Keywords: noncommutative geometry; Gauss–Bonnet; spectral triple.
Received: December 9, 2014; in final form September 17, 2015; Published online September 26, 2015
Bibliographic databases:
Document Type: Article
MSC: 58B34; 46L87
Language: English
Citation: Ludwik Dąbrowski, Andrzej Sitarz, “An Asymmetric Noncommutative Torus”, SIGMA, 11 (2015), 075, 11 pp.
Citation in format AMSBIB
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\paper An Asymmetric Noncommutative Torus
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    		Symmetry, Integrability and Geometry: Methods and Applications
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