spo(2|2)-Equivariant Quantizations on the Supercircle S¹|²
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
spo(2|2)-Equivariant Quantizations on the Supercircle S¹|²
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| Creator |
Mellouli, N.
Nibirantiza, A. Radoux, F. |
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| Description |
We consider the space of differential operators Dλμ acting between λ- and μ-densities defined on S¹|² endowed with its standard contact structure. This contact structure allows one to define a filtration on Dλμ which is finer than the classical one, obtained by writting a differential operator in terms of the partial derivatives with respect to the different coordinates. The space Dλμ and the associated graded space of symbols Sδ (δ=μ−λ) can be considered as spo(2|2)-modules, where spo(2|2) is the Lie superalgebra of contact projective vector fields on S¹|². We show in this paper that there is a unique isomorphism of spo(2|2)-modules between Sδ and Dλμ that preserves the principal symbol (i.e. an spo(2|2)-equivariant quantization) for some values of δ called non-critical values. Moreover, we give an explicit formula for this isomorphism, extending in this way the results of [Mellouli N., SIGMA 5 (2009), 111, 11 pages] which were established for second-order differential operators. The method used here to build the spo(2|2)-equivariant quantization is the same as the one used in [Mathonet P., Radoux F., Lett. Math. Phys. 98 (2011), 311-331] to prove the existence of a pgl(p+1|q)-equivariant quantization on Rp|q.
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| Date |
2019-02-21T07:08:09Z
2019-02-21T07:08:09Z 2013 |
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| Type |
Article
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| Identifier |
spo(2|2)-Equivariant Quantizations on the Supercircle S¹|² / N. Mellouli, A. Nibirantiza, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 27 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53D10; 17B66; 17B10 DOI: http://dx.doi.org/10.3842/SIGMA.2013.055 http://dspace.nbuv.gov.ua/handle/123456789/149350 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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