జర్నల్ ఆఫ్ జెనరలైజ్డ్ లై థియరీ అండ్ అప్లికేషన్స్

On the First aff(1)-Relative Cohomology of the Lie Algebra of Vector Fields and Differential Operators

Abstract

Meher A

Let Vect(1) be the Lie algebra of smooth vector fields on 1. In this paper, we classify aff(1) -invariant linear differential operators from Vect(1) to λ,μ;v vanishing on aff(1), where λ,μ;v≔Homdiff(λ⊗μ;v) is the space of bilinear differential operators acting on weighted densities. This result allows us to compute the first differential aff(1)-relative cohomology of Vect(1) with coefficients in λ,μ;v