scholarly journals Space of Second-Order Linear Differential Operators as a Module over the Lie Algebra of Vector Fields

1997 ◽  
Vol 132 (2) ◽  
pp. 316-333 ◽  
Author(s):  
C. Duval ◽  
V.Yu. Ovsienko
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Differential Operators ◽  
Second Order ◽  
Order Linear ◽  
Linear Differential Operators ◽  
Linear Differential

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

2019 ◽  
Vol 56 (3) ◽  
pp. 280-296
Author(s):  
Abdaoui Meher
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Differential Operators ◽  
Smooth Vector ◽  
Linear Differential Operators ◽  
Relative Cohomology ◽  
Linear Differential

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 .

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