Differential ‘Galois’ extensions with new constants

Lourdes Juan; Andy R. Magid

doi:10.1016/j.crma.2010.04.004

Algebra/Ordinary Differential Equations

Differential ‘Galois’ extensions with new constants

Presented by: Bernard Malgrange

Lourdes Juan ¹; Andy R. Magid ²

¹Department of Mathematics, Texas Tech University, Lubbock, TX 79409, United States
²Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States

Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 487-490

Abstract (Original language)
Résumé

Let F be a differential field with algebraically closed field of constants $C$ and let E be a differential field extension of F. The field E is a differential Galois extension if it is generated over F by a full set of solutions of a linear homogeneous differential equation with coefficients in F and if its field of constants coincides with $C$ . We study the differential field extensions of F that satisfy the first condition but not the second.

Soit F un corps différentiel dont le corps des constantes $C$ est algébriquement clos et soit $E \supset F$ une extension de corps différentiels. Le corps différentiel E est une extension galoisienne différentielle de F s'il est engendré sur F par une base de solutions d'une équation différentielle linéaire homogène à coefficients dans F et si son corps des constantes est $C$ . Nous étudions les extensions différentielles de F qui satisfont la première condition et non la seconde.

Received: 2009-02-12
Accepted: 2010-04-06
Published online: 2010-04-27

DOI: 10.1016/j.crma.2010.04.004

Author's affiliations:

Lourdes Juan ¹ ; Andy R. Magid ²

¹ Department of Mathematics, Texas Tech University, Lubbock, TX 79409, United States
² Department of Mathematics, University of Oklahoma, Norman, OK 73019, United States

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     author = {Lourdes Juan and Andy R. Magid},
     title = {Differential {{\textquoteleft}Galois{\textquoteright}} extensions with new constants},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {487--490},
     year = {2010},
     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2010.04.004},
     language = {en},
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Lourdes Juan; Andy R. Magid. Differential ‘Galois’ extensions with new constants. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 487-490. doi: 10.1016/j.crma.2010.04.004

References
Cited by

[1] L. Juan; A. Ledet Equivariant vector fields on non-trivial ${SO}_{n}$ -torsors and differential Galois theory, Journal of Algebra, Volume 316 (2007), pp. 735-745

[2] A. Magid Lectures on Differential Galois Theory, University Lecture Series, vol. 7, American Mathematical Society, Providence RI, 1997 (second printing with corrections)

[3] M. van der Put; M. Singer Differential Galois Theory, Springer-Verlag, New York, 2003

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