Natural and Projectively Invariant Quantizations on Supermanifolds
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146803 |
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| Cite this: | Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862556690600165376 |
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| author | Leuther, T. Radoux, F. |
| author_facet | Leuther, T. Radoux, F. |
| citation_txt | Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two.
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| first_indexed | 2025-11-25T22:33:36Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146803 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:33:36Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Leuther, T. Radoux, F. 2019-02-11T15:28:17Z 2019-02-11T15:28:17Z 2011 Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53B05; 53B10; 53D50; 58A50 DOI:10.3842/SIGMA.2011.034 https://nasplib.isofts.kiev.ua/handle/123456789/146803 The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two. It is a pleasure to thank P. Mathonet for fruitful discussions. We also thank the referees for
 suggestions leading to great improvements of the original paper. Finally, F. Radoux thanks the Belgian FNRS for his research fellowship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Natural and Projectively Invariant Quantizations on Supermanifolds Article published earlier |
| spellingShingle | Natural and Projectively Invariant Quantizations on Supermanifolds Leuther, T. Radoux, F. |
| title | Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_full | Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_fullStr | Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_full_unstemmed | Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_short | Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_sort | natural and projectively invariant quantizations on supermanifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146803 |
| work_keys_str_mv | AT leuthert naturalandprojectivelyinvariantquantizationsonsupermanifolds AT radouxf naturalandprojectivelyinvariantquantizationsonsupermanifolds |