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Quantum Isometry Group for Spectral Triples with Real Structure
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Quantum Isometry Group for Spectral Triples with Real Structure
Інший ID:
2010 Mathematics Subject Classification: 58B32
Посилання:
Quantum Isometry Group for Spectral Triples with Real Structure / D. Goswami // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — англ.
Підтримка:
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.
Дата:
2010
Переглядів:
565
Завантажень:
241
Анотація:
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].
