no. 4
Differential Galois realization of double covers
[Réalisation galoisienne différentielle de revêtements doubles]
Crespo, Teresa1 ; Hajto, Zbigniew2
1 Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran via de les Corts Catalanes 585, 08007 Barcelona (Espagne)
2 Akademia Rolnicza, Zaklad Matematyki, al. Mickiewicza 24/28, 30-059 Kraków (Pologne)
Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1017-1025.

Nous présentons une construction effective d’équations différentielles linéaires homogènes d’ordre 2 à groupe de Galois 2A 4 ,2S 4 ou 2A 5 .

An effective construction of homogeneous linear differential equations of order 2 with Galois group 2A 4 ,2S 4 or 2A 5 is presented.

DOI : 10.5802/aif.1908
Classification : 12H05, 11F80, 12F12
Keywords: Picard-Vessiot extension, symmetric square of a differential equation, group representations
Mot clés : extension de Picard-Vessiot, carré symétrique d'une équation différentielle, représentations de groupes

Crespo, Teresa 1 ; Hajto, Zbigniew 2

1 Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran via de les Corts Catalanes 585, 08007 Barcelona (Espagne)
2 Akademia Rolnicza, Zaklad Matematyki, al. Mickiewicza 24/28, 30-059 Kraków (Pologne) 
@article{AIF_2002__52_4_1017_0,
     author = {Crespo, Teresa and Hajto, Zbigniew},
     title = {Differential {Galois} realization of double covers},
     journal = {Annales de l'Institut Fourier},
     pages = {1017--1025},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {52},
     number = {4},
     year = {2002},
     doi = {10.5802/aif.1908},
     zbl = {1017.12005},
     mrnumber = {1926670},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1908/}
}
TY  - JOUR
AU  - Crespo, Teresa
AU  - Hajto, Zbigniew
TI  - Differential Galois realization of double covers
JO  - Annales de l'Institut Fourier
PY  - 2002
SP  - 1017
EP  - 1025
VL  - 52
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1908/
DO  - 10.5802/aif.1908
LA  - en
ID  - AIF_2002__52_4_1017_0
ER  - 
%0 Journal Article
%A Crespo, Teresa
%A Hajto, Zbigniew
%T Differential Galois realization of double covers
%J Annales de l'Institut Fourier
%D 2002
%P 1017-1025
%V 52
%N 4
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1908/
%R 10.5802/aif.1908
%G en
%F AIF_2002__52_4_1017_0
Crespo, Teresa; Hajto, Zbigniew. Differential Galois realization of double covers. Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1017-1025. doi : 10.5802/aif.1908. https://aif.centre-mersenne.org/articles/10.5802/aif.1908/

[1] T. Crespo; Z. Hajto Finite linear groups as differential Galois groups, Bull. Pol. Ac. Math, Volume 49 (2001) no. 4, pp. 363-375 | MR | Zbl

[2] T. Crespo; Z. Hajto Primitive unimodular groups of degree 2 as differential Galois groups, J. of Algebra, Volume 229 (2000), pp. 678-694 | DOI | MR | Zbl

[3] T. Crespo; Z. Hajto Recouvrements doubles comme groupes de Galois différentiels, C.R. Acad. Sci. Paris, Série I, Volume 333 (2001), pp. 271-274 | MR | Zbl

[4] I. Kaplansky An introduction to differential algebra, Hermann, 1976 | MR | Zbl

[5] A.R. Magid Lectures on differential Galois theory, A.M.S (1997) | Zbl

[6] G. Malle; B.H. Matzat Inverse Galois Theory, Springer-Verlag, Berlin, 1999 | MR | Zbl

[7] G.A. Miller; H.F. Blichfeldt; L.E. Dickson Theory and applications of finite groups, John Wiley and sons, Inc., 1916 | JFM

[8] J-P. Serre L'invariant de Witt de la forme Tr (x 2 ), Comment. Math. Helvetici, Volume 59 (1984), pp. 651-676 | MR | Zbl

[9] J-P. Serre Cohomologie galoisienne, Springer Verlag, 1994 | MR | Zbl

[10] M.F. Singer; E. Tournier ed. An outline of differential Galois theory, Computer Algebra and Differential Equations (1989), pp. 3-57 | Zbl

[11] M.F. Singer; F. Ulmer Galois groups of second and third order linear differential equations, Journal of Symbolic Computation, Volume 16 (1993), pp. 9-36 | DOI | MR | Zbl

Cité par Sources :