Spectral Distances: Results for Moyal Plane and Noncommutative Torus
The spectral distance for noncommutative Moyal planes is considered in the framework of a non compact spectral triple recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit formula for the distance between any two elements of a particular class of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146321 |
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| Cite this: | Spectral Distances: Results for Moyal Plane and Noncommutative Torus / E. Cagnache, J.C. Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. |
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Cagnache, E. Wallet, J.C. 2019-02-08T20:53:46Z 2019-02-08T20:53:46Z 2010 Spectral Distances: Results for Moyal Plane and Noncommutative Torus / E. Cagnache, J.C. Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B34; 46L52; 81T75 DOI:10.3842/SIGMA.2010.026 https://nasplib.isofts.kiev.ua/handle/123456789/146321 The spectral distance for noncommutative Moyal planes is considered in the framework of a non compact spectral triple recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit formula for the distance between any two elements of a particular class of pure states can be determined. The corresponding result is discussed. The existence of some pure states at infinite distance signals that the topology of the spectral distance on the space of states is not the weak * topology. The case of the noncommutative torus is also considered and a formula for the spectral distance between some states is also obtained. This paper is a contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 18–20, 2009, Prague, Czech Republic). The full collection is available at http://www.emis.de/journals/SIGMA/ISQS2009.html. One of us (E.C.) thanks the organizers of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries for their kind invitation which motivated the present paper. We thank the referees for their fruitful suggestions and comments that helped us to improve the initial version of this paper. Discussions and correspondence on various metric aspects of noncommutative geometry with F. d’Andrea and P. Martinetti are gratefully acknowledged. One of us (JCW) thanks F. Lizzi and B. Iochum for discussions and comments. We thank E. Jolibois for discussions at various stage of this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spectral Distances: Results for Moyal Plane and Noncommutative Torus Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| spellingShingle |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus Cagnache, E. Wallet, J.C. |
| title_short |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| title_full |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| title_fullStr |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| title_full_unstemmed |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| title_sort |
spectral distances: results for moyal plane and noncommutative torus |
| author |
Cagnache, E. Wallet, J.C. |
| author_facet |
Cagnache, E. Wallet, J.C. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The spectral distance for noncommutative Moyal planes is considered in the framework of a non compact spectral triple recently proposed as a possible noncommutative analog of non compact Riemannian spin manifold. An explicit formula for the distance between any two elements of a particular class of pure states can be determined. The corresponding result is discussed. The existence of some pure states at infinite distance signals that the topology of the spectral distance on the space of states is not the weak * topology. The case of the noncommutative torus is also considered and a formula for the spectral distance between some states is also obtained.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146321 |
| citation_txt |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus / E. Cagnache, J.C. Wallet // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. |
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AT cagnachee spectraldistancesresultsformoyalplaneandnoncommutativetorus AT walletjc spectraldistancesresultsformoyalplaneandnoncommutativetorus |
| first_indexed |
2025-11-30T23:10:30Z |
| last_indexed |
2025-11-30T23:10:30Z |
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1850858762630332417 |