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The Fourth-Linear aff ( 1 ) -Invariant Differential Operators and the First Cohomology of the Lie Algebra of Vector Fields on RP 1

Author

Listed:
  • Areej A. Almoneef

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Meher Abdaoui

    (Department of Mathematics, College of Sciences and Humanities-Kowaiyia, Shaqra University, Shaqra 15526, Saudi Arabia)

  • Abderraouf Ghallabi

    (Department of Mathematics, Faculty of Sciences of Sfax, BP 802, Sfax 3038, Tunisia)

Abstract

In this paper, we denote the Lie algebra of smooth vector fields on RP 1 by V ( RP 1 ) . This paper focuses on two parts. In the beginning, we determine the cohomology space of aff ( 1 ) with coefficients in D τ , λ , μ ; ν . Afterward, we classify aff ( 1 ) -invariant fourth-linear differential operators from V ( RP 1 ) to D τ , λ , μ ; ν vanishing on aff ( 1 ) . This result enables us to compute the aff ( 1 ) -relative cohomology of V ( RP 1 ) with coefficients in D τ , λ , μ ; ν .

Suggested Citation

  • Areej A. Almoneef & Meher Abdaoui & Abderraouf Ghallabi, 2023. "The Fourth-Linear aff ( 1 ) -Invariant Differential Operators and the First Cohomology of the Lie Algebra of Vector Fields on RP 1," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1226-:d:1085910
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