Conformal symbols and the action of contact vector fields over the superline
Let 𝒦 be the Lie superalgebra of contact vector fields on the supersymmetric line . We compute the action of 𝒦 on the modules of differential and pseudo-differential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols,...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2009; no. 633; pp. 115 - 163 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Walter de Gruyter GmbH & Co. KG
01.08.2009
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| Online Access | Get full text |
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| Summary: | Let 𝒦 be the Lie superalgebra of contact vector fields on the supersymmetric line . We compute the action of 𝒦 on the modules of differential and pseudo-differential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols, 1-cohomology, and various uniserial subquotients of these modules. We also outline the computation of the 𝒦-equivalences and symmetries of their subquotients. |
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| Bibliography: | istex:FD4EDE0E61E0B1FDCA90CC483CDF7C80DA8E27A8 crelle.2009.062.pdf ArticleID:CRLL.2009.633.115 ark:/67375/QT4-2VCGDDLB-2 |
| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/CRELLE.2009.062 |