Quantum Dimension and Quantum Projective Spaces
We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dąbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K₂ρ or its inverse. The spectral dimensio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146544 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quantum Dimension and Quantum Projective Spaces / M. Matassa // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725033337552896 |
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| author | Matassa, M. |
| author_facet | Matassa, M. |
| citation_txt | Quantum Dimension and Quantum Projective Spaces / M. Matassa // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dąbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K₂ρ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.
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| first_indexed | 2025-12-07T18:50:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146544 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:50:34Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Matassa, M. 2019-02-09T21:11:52Z 2019-02-09T21:11:52Z 2014 Quantum Dimension and Quantum Projective Spaces / M. Matassa // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58J42; 58B32; 46L87 DOI:10.3842/SIGMA.2014.097 https://nasplib.isofts.kiev.ua/handle/123456789/146544 We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dąbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K₂ρ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out. I wish to thank Jens Kaad for helpful comments on a first version of this paper. I also want to
 thank the anonymous referees, whose observations have improved this presentation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Dimension and Quantum Projective Spaces Article published earlier |
| spellingShingle | Quantum Dimension and Quantum Projective Spaces Matassa, M. |
| title | Quantum Dimension and Quantum Projective Spaces |
| title_full | Quantum Dimension and Quantum Projective Spaces |
| title_fullStr | Quantum Dimension and Quantum Projective Spaces |
| title_full_unstemmed | Quantum Dimension and Quantum Projective Spaces |
| title_short | Quantum Dimension and Quantum Projective Spaces |
| title_sort | quantum dimension and quantum projective spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146544 |
| work_keys_str_mv | AT matassam quantumdimensionandquantumprojectivespaces |