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Second-Order Conformally Equivariant Quantization in Dimension 1|2
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 equip...
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Інститут математики НАН України
2009
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149129 |
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irk-123456789-1491292019-02-20T01:26:23Z Second-Order Conformally Equivariant Quantization in Dimension 1|2 Mellouli, N. 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. 2009 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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English |
| 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. |
| format |
Article |
| author |
Mellouli, N. |
| spellingShingle |
Mellouli, N. Second-Order Conformally Equivariant Quantization in Dimension 1|2 Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mellouli, N. |
| author_sort |
Mellouli, N. |
| title |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
| title_short |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
| title_full |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
| title_fullStr |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
| title_full_unstemmed |
Second-Order Conformally Equivariant Quantization in Dimension 1|2 |
| title_sort |
second-order conformally equivariant quantization in dimension 1|2 |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149129 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT melloulin secondorderconformallyequivariantquantizationindimension12 |
| first_indexed |
2023-05-20T17:32:11Z |
| last_indexed |
2023-05-20T17:32:11Z |
| _version_ |
1796153523181715456 |