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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
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
Citation:
Ludwik Dąbrowski, Andrzej Sitarz, “An Asymmetric Noncommutative Torus”, SIGMA, 11 (2015), 075, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1056 https://www.mathnet.ru/eng/sigma/v11/p75
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Abstract page: | 162 | Full-text PDF : | 33 | References: | 25 |
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