An Asymmetric Noncommutative Torus

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 no...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2015
Main Authors: Dąbrowski, L., Sitarz, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147144
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:An Asymmetric Noncommutative Torus / L. Dąbrowski, A. Sitarz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Dąbrowski, L.
Sitarz, A.
author_facet Dąbrowski, L.
Sitarz, A.
citation_txt An Asymmetric Noncommutative Torus / L. Dąbrowski, A. Sitarz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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).
first_indexed 2025-11-30T12:59:19Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-30T12:59:19Z
publishDate 2015
publisher Інститут математики НАН України
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spelling Dąbrowski, L.
Sitarz, A.
2019-02-13T17:27:07Z
2019-02-13T17:27:07Z
2015
An Asymmetric Noncommutative Torus / L. Dąbrowski, A. Sitarz // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 58B34; 46L87
DOI:10.3842/SIGMA.2015.075
https://nasplib.isofts.kiev.ua/handle/123456789/147144
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).
L.D. gratefully acknowledges the hospitality of the Institute of Physics, Jagiellonian University
 in Krak´ow. L.D. partially supported by PRIN 2010 grant “Operator Algebras, Noncommutative
 Geometry and Applications”, A.S. partially supported by NCN grant 2012/06/M/ST1/00169.
 The authors express their gratitude to the referees for valuable comments.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
An Asymmetric Noncommutative Torus
Article
published earlier
spellingShingle An Asymmetric Noncommutative Torus
Dąbrowski, L.
Sitarz, A.
title An Asymmetric Noncommutative Torus
title_full An Asymmetric Noncommutative Torus
title_fullStr An Asymmetric Noncommutative Torus
title_full_unstemmed An Asymmetric Noncommutative Torus
title_short An Asymmetric Noncommutative Torus
title_sort asymmetric noncommutative torus
url https://nasplib.isofts.kiev.ua/handle/123456789/147144
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AT sitarza anasymmetricnoncommutativetorus
AT dabrowskil asymmetricnoncommutativetorus
AT sitarza asymmetricnoncommutativetorus