Natural and Projectively Invariant Quantizations on Supermanifolds

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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dc.contributor.author	Leuther, T.
dc.contributor.author	Radoux, F.
dc.date.accessioned	2019-02-11T15:28:17Z
dc.date.available	2019-02-11T15:28:17Z
dc.date.issued	2011
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 53B05; 53B10; 53D50; 58A50
dc.identifier.other	DOI:10.3842/SIGMA.2011.034
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146803
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Natural and Projectively Invariant Quantizations on Supermanifolds	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA