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Cohomology of the vector fields lie algebras on ℝℙ1 acting on bilinear differential operators

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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… Click to show full abstract

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 .

Keywords: cohomology vector; bilinear differential; vector fields; fields lie; differential operators

Journal Title: Studia Scientiarum Mathematicarum Hungarica
Year Published: 2019

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