Abstract
Let Vect(R) be the Lie algebra of smooth vector fields on R and D-lambda,D-mu;nu := Hom(diff)(F-lambda circle times F-mu, F-nu) be the space of bilinear differential operators acting on weighted densities. In this paper, we classify sl(2)-invariant skew-symmetric binary differential operators from Vect(R) boolean AND Vect(R) to D-lambda,D-mu;nu vanishing on sl(2). This result allows us to compute the second differential sl(2)-relative cohomology of Vect(R) with coefficients in D-lambda,D-mu;nu.