The Fourth-Linear aff(1)-Invariant Differential Operators and the First Cohomology of the Lie Algebra of Vector Fields on RP1

被引：0
|
作者：
Almoneef, Areej A. [1 ]
Abdaoui, Meher [2 ]
Ghallabi, Abderraouf [3 ]
机构：
[1] Princess Nourah bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia
[2] Shaqra Univ, Coll Sci & Humanities Kowaiyia, Dept Math, Shaqra 15526, Saudi Arabia
[3] Fac Sci Sfax, Dept Math, BP 802, Sfax 3038, Tunisia
来源：
MATHEMATICS | 2023年 / 11卷 / 05期
关键词：
invariant differential operators; Lie algebra of vector fields; cohomology;
D O I：
10.3390/math11051226
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we denote the Lie algebra of smooth vector fields on RP(1 )by V(RP1). This paper focuses on two parts. In the beginning, we determine the cohomology space of aff(1) with coefficients in D-tau,D-lambda,D-mu;nu. Afterward, we classify aff(1)-invariant fourth-linear differential operators from V(RP1) to D-tau,D-lambda,D-mu;nu vanishing on aff(1). This result enables us to compute the aff(1)-relative cohomology of V(RP1) with coefficients inD(tau,lambda,mu;nu).
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页数：16
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