On sl(2,R)-relative cohomology of the Lie algebra of vector fields and differential operators
Abstract
Description
Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T^* R) admits a non-trivial deformation (given by differential operators on weighted densities) as a Vect(R)-module that becomes trivial once the action is restricted to sl(2). The deformations of Pol(T^* R), which become trivial once the action is restricted to sl(2) and such that the Vect(R)-action on them is expressed in terms of differential operators, are classified by the elements of the weight basis of H^2(Vect(R),sl(2);D_{λ,μ}). The main result of this paper is computation of this cohomology. In addition to relative cohomology, we exhibit 2-cocycles spanning H^2(g; D_{λ,μ}) for g=Vect(R) and sl(2).
official version
official version