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

Sofiane Bouarroudj

doi:10.1142/S0219887805000430

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

Sofiane Bouarroudj

Mathematics

Research output: Contribution to journal › Article › peer-review

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, D_λ,ν;μ, 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 D_λ,ν;μ.

Original language	English (US)
Pages (from-to)	23-40
Number of pages	18
Journal	International Journal of Geometric Methods in Modern Physics
Volume	2
Issue number	1
DOIs	https://doi.org/10.1142/S0219887805000430
State	Published - Feb 2005

Keywords

Cohomology of Lie algebras
Differential operators on tensor densities
Transvectants
sl(2, ℝ)-invariant operators

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887805000430

Cite this

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