Differential Galois realization of double covers
Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1017-1025.

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

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

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)
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Crespo, Teresa; Hajto, Zbigniew. Differential Galois realization of double covers. Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1017-1025. doi : 10.5802/aif.1908. http://archive.numdam.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

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