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Cohomology of the vector fields lie algebras on ℝℙ1 acting on bilinear differential operators
Let Vect (ℝℙ1) be the Lie algebra of smooth vector fields on ℝℙ1. In this paper, we classify -invariant linear differential operators from Vect (ℝℙ1) to vanishing on , where is the space of bilinear differential operators acting on weighted densities. This result allows us to compute the first differential -relative cohomology of Vect (ℝℙ1) with coefficients in .
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