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 |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| 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| _version_ | 1862632413865181184 |
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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).
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| first_indexed | 2025-11-30T12:59:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147144 |
| 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 |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT dabrowskil anasymmetricnoncommutativetorus AT sitarza anasymmetricnoncommutativetorus AT dabrowskil asymmetricnoncommutativetorus AT sitarza asymmetricnoncommutativetorus |