Second-Order Conformally Equivariant Quantization in Dimension 1|2
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Second-Order Conformally Equivariant Quantization in Dimension 1|2
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| Creator |
Mellouli, N.
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| Description |
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.
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| Date |
2019-02-19T17:34:36Z
2019-02-19T17:34:36Z 2009 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2000 Mathematics Subject Classification: 17B10; 17B68; 53D55 http://dspace.nbuv.gov.ua/handle/123456789/149129 |
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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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