Quantum Isometry Group for Spectral Triples with Real Structure
Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and references therein, we prove that there is always...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146117 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quantum Isometry Group for Spectral Triples with Real Structure / D. Goswami // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Goswami, D. 2019-02-07T14:43:33Z 2019-02-07T14:43:33Z 2010 Quantum Isometry Group for Spectral Triples with Real Structure / D. Goswami // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B32 https://nasplib.isofts.kiev.ua/handle/123456789/146117 Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and references therein, we prove that there is always a universal object in the category of compact quantum group acting by orientation preserving isometries (in the sense of [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572]) and also preserving the real structure of the spectral triple. This gives a natural definition of quantum isometry group in the context of real spectral triples without fixing a choice of 'volume form' as in [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572]. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html. The author acknowledges the support from Indian National Science Academy for the project ‘Noncommutative Geometry and Quantum Groups’ and UKIERI, British Council. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Isometry Group for Spectral Triples with Real Structure Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Quantum Isometry Group for Spectral Triples with Real Structure |
| spellingShingle |
Quantum Isometry Group for Spectral Triples with Real Structure Goswami, D. |
| title_short |
Quantum Isometry Group for Spectral Triples with Real Structure |
| title_full |
Quantum Isometry Group for Spectral Triples with Real Structure |
| title_fullStr |
Quantum Isometry Group for Spectral Triples with Real Structure |
| title_full_unstemmed |
Quantum Isometry Group for Spectral Triples with Real Structure |
| title_sort |
quantum isometry group for spectral triples with real structure |
| author |
Goswami, D. |
| author_facet |
Goswami, D. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and references therein, we prove that there is always a universal object in the category of compact quantum group acting by orientation preserving isometries (in the sense of [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572]) and also preserving the real structure of the spectral triple. This gives a natural definition of quantum isometry group in the context of real spectral triples without fixing a choice of 'volume form' as in [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572].
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146117 |
| citation_txt |
Quantum Isometry Group for Spectral Triples with Real Structure / D. Goswami // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — англ. |
| work_keys_str_mv |
AT goswamid quantumisometrygroupforspectraltripleswithrealstructure |
| first_indexed |
2025-12-07T16:27:44Z |
| last_indexed |
2025-12-07T16:27:44Z |
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1850867569759617024 |