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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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146321 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1463212019-02-09T01:23:44Z Spectral Distances: Results for Moyal Plane and Noncommutative Torus Cagnache, E. Wallet, J.C. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146321 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cagnache, E. Wallet, J.C. |
| spellingShingle |
Cagnache, E. Wallet, J.C. Spectral Distances: Results for Moyal Plane and Noncommutative Torus Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cagnache, E. Wallet, J.C. |
| author_sort |
Cagnache, E. |
| title |
Spectral Distances: Results for Moyal Plane and Noncommutative Torus |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT cagnachee spectraldistancesresultsformoyalplaneandnoncommutativetorus AT walletjc spectraldistancesresultsformoyalplaneandnoncommutativetorus |
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2023-05-20T17:24:05Z |
| last_indexed |
2023-05-20T17:24:05Z |
| _version_ |
1796153214727356416 |