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dc.contributor.author |
Mellouli, N. |
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dc.date.accessioned |
2019-02-19T17:34:36Z |
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dc.date.available |
2019-02-19T17:34:36Z |
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dc.date.issued |
2009 |
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dc.identifier.citation |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 / N. Mellouli // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 14 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2000 Mathematics Subject Classification: 17B10; 17B68; 53D55 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/149129 |
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dc.description.abstract |
This paper is the next step of an ambitious program to develop conformally equivariant quantization on supermanifolds. This problem was considered so far in (super)dimensions 1 and 1|1. We will show that the case of several odd variables is much more difficult. We consider the supercircle S1|2 equipped with the standard contact structure. The conformal Lie superalgebra K(2) of contact vector fields on S1|2 contains the Lie superalgebra osp(2|2). We study the spaces of linear differential operators on the spaces of weighted densities as modules over osp(2|2). We prove that, in the non-resonant case, the spaces of second order differential operators are isomorphic to the corresponding spaces of symbols as osp(2|2)-modules. We also prove that the conformal equivariant quantization map is unique and calculate its explicit formula. |
uk_UA |
dc.description.sponsorship |
I am grateful to H. Gargoubi and V. Ovsienko for the statement of the problem and constant help. I am also pleased to thank D. Leites for critical reading of this paper and a number of helpful suggestions. |
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 |
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dc.title |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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