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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn021, 19 pages, doi:10.1093/imrn/rnn021 published on May 1, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Supertransvectants and Symplectic Geometry

H. Gargoubi1 and V. Ovsienko2

1 Institut Préeparatoire Aux Etudes d'lngéenieurs, 2 Rue Jawaher Lel Nehru, Monfleury 1008 Tunis, Tunisia
2 Centre National de la Recherche Scientifique, Institut Camille Jordan, Universit ée Claude Bernard Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne Cedex, France

Correspondence: Correspondence to be sent to: hichem.gargoubi{at}ipeit.rnu.tn

The 1|1-supertransvectants are the osp(1|2)-invariant bilinear operations on weighted densities on the supercircle S1|1, the projective version of Formula . These operations are analogues of the famous Gordan transvectants (or Rankin–Cohen brackets). We prove that supertransvectants coincide with the iterated Poisson and ghost Poisson brackets on Formula and apply this result to construct star-products.


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