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

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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, Dλ,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 Dλ,ν;μ.

Original languageEnglish (US)
Pages (from-to)23-40
Number of pages18
JournalInternational Journal of Geometric Methods in Modern Physics
Issue number1
StatePublished - Feb 2005


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

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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