Cohomology of the vector fields Lie algebras on ℝ acting on trilinear differential operators, vanishing on 𝔞𝔣𝔣(1)

Abstract

The main topic of this paper is to compute the first relative cohomology group of the Lie algebra of smooth vector fields [Formula: see text], with coefficients in the space of trilinear differential operators that act on tensor densities, [Formula: see text], vanishing on the Lie algebra [Formula: see text].