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 APM  Vol.9 No.11 , November 2019
Some Properties of First Order Differential Operators
Abstract: We study some properties of first order differential operators from an algebraic viewpoint. We show this last can be decomposed in sum of an element of a module and a derivation. From a geometric viewpoint, we give some properties on the algebra of smooth functions. The Dirac mass at a point is the best example of first order differential operators at this point. This allows to construct a basis of this set and its dual basis.
Cite this paper: Gatse, S. (2019) Some Properties of First Order Differential Operators. Advances in Pure Mathematics, 9, 934-943. doi: 10.4236/apm.2019.911046.
References

[1]   Okassa, E. (2007) Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi. Journal of Pure and Applied Algebra, 208, 1071-1089.
https://doi.org/10.1016/j.jpaa.2006.05.013

[2]   Bourbaki, N. (1970) Algèbre, chapitres 1 à 3. Hermann, Paris.

[3]   Okassa, E. (2008) On Lie-Rinehart-Jacobi Algebras. Journal of Algebra and Its Applications, 7, 749-772.
https://doi.org/10.1142/S0219498808003107

[4]   Rinehart, G. (1963) Differential Forms for General Commutative Algebras. Transactions of the American Mathematical Society, 108, 195-222.
https://doi.org/10.1090/S0002-9947-1963-0154906-3

[5]   Gatsé, S.C. (2016) Hamiltonian Vector Field on Locally Conformally Symplectic Manifold. International Mathematical Forum, 11, 933-941.
https://doi.org/10.12988/imf.2016.6666

 
 
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