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

Areej A. Almoneef (), Meher Abdaoui and Abderraouf Ghallabi
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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

Mathematics, 2023, vol. 11, issue 5, 1-16

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 .

Keywords: invariant differential operators; Lie algebra of vector fields; cohomology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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