Skip to content
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
From the journal

Abstract

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