no. 9-10
Algebra/Ordinary Differential Equations
Differential ‘Galois’ extensions with new constants
[Extensions différentielles « galoisiennes » avec nouvelles constantes]

Présenté par : Bernard Malgrange

Juan, Lourdes1 ; Magid, Andy R.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
Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 487-490.

Soit F un corps différentiel dont le corps des constantes C est algébriquement clos et soit E⊃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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.04.004
Juan, Lourdes 1 ; Magid, Andy R. 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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     title = {Differential {{\textquoteleft}Galois{\textquoteright}} extensions with new constants},
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Juan, Lourdes; Magid, Andy R. Differential ‘Galois’ extensions with new constants. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 487-490. doi : 10.1016/j.crma.2010.04.004. http://www.numdam.org/articles/10.1016/j.crma.2010.04.004/

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

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

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

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