COHOMOLOGY OF THE VECTOR FIELDS LIE ALGEBRAS ON ℝℙ1 ACTING ON BILINEAR DIFFERENTIAL OPERATORS

Abstract

The main topic of this paper is two-fold. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(ℝℙ1), with coefficients in the space of bilinear differential operators that act on tensor densities, [Formula: see text], vanishing on the Lie algebra sl(2, ℝ). Second, we compute the first cohomology group of the Lie algebra sl(2, ℝ) with coefficients in [Formula: see text].