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Licensed Unlicensed Requires Authentication Published by De Gruyter June 16, 2009

Conformal symbols and the action of contact vector fields over the superline

  • Charles H. Conley


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.

Received: 2007-12-10
Revised: 2008-03-23
Published Online: 2009-06-16
Published in Print: 2009-August

© Walter de Gruyter Berlin · New York 2009

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