Universal Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 1, Pages 25 - 47
(June 2017) http://dx.doi.org/10.17654/UM010010025 |
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ON HOW TO SUPERIZE THE SPACES OF DIFFERENTIAL OPERATORS ON THE CONTACT MANIFOLDS ![](/admin/tinymce_uploads/2aug93on_how8.gif)
Aboubacar Nibirantiza
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Abstract: We study the existence of three types of filtrations of the space of differential operators on the superspaces endowed with the standard contact structure a. On we have the first filtration called canonical and because of the existence of the contact structure on superspaces , we obtain the second filtration on the space called filtration of Heisenberg and thus the space is therefore denoted by We have also a new filtration induced on by the two filtrations and it is called bifiltration. Explicitly, the space of differential operators is filtered canonically by the order of its differential operators. When it is filtered by the order of Heisenberg, the order of any differential operator is equal to This study is the generalization, in super case, of the model studied by Conley and Ovsienko in [3]. Finally,we show that the -module structure on the space of differential operators is induced on the space and therefore on the associated space of normal symbols, and also on the space of symbols of Heisenberg and on the space of fine symbol ![](/admin/tinymce_uploads/2aug103we_stu18.gif)
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Keywords and phrases: contact structure on superspaces, supergeometry, differential operators. |
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