Differential Galois realization of double covers

Teresa Crespo[1]; Zbigniew Hajto[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)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 4, page 1017-1025
  • ISSN: 0373-0956

Abstract

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

How to cite

top

Crespo, Teresa, and Hajto, Zbigniew. "Differential Galois realization of double covers." Annales de l’institut Fourier 52.4 (2002): 1017-1025. <http://eudml.org/doc/116000>.

@article{Crespo2002,
abstract = {An effective construction of homogeneous linear differential equations of order 2 with Galois group $2A_4, 2S_4$ or $2A_5$ is presented.},
affiliation = {Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran via de les Corts Catalanes 585, 08007 Barcelona (Espagne); Akademia Rolnicza, Zaklad Matematyki, al. Mickiewicza 24/28, 30-059 Kraków (Pologne)},
author = {Crespo, Teresa, Hajto, Zbigniew},
journal = {Annales de l’institut Fourier},
keywords = {Picard-Vessiot extension; symmetric square of a differential equation; group representations; differential Galois group; alternating groups; symmetric group; double covers; differential field of characteristic 0},
language = {eng},
number = {4},
pages = {1017-1025},
publisher = {Association des Annales de l'Institut Fourier},
title = {Differential Galois realization of double covers},
url = {http://eudml.org/doc/116000},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Crespo, Teresa
AU - Hajto, Zbigniew
TI - Differential Galois realization of double covers
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 4
SP - 1017
EP - 1025
AB - An effective construction of homogeneous linear differential equations of order 2 with Galois group $2A_4, 2S_4$ or $2A_5$ is presented.
LA - eng
KW - Picard-Vessiot extension; symmetric square of a differential equation; group representations; differential Galois group; alternating groups; symmetric group; double covers; differential field of characteristic 0
UR - http://eudml.org/doc/116000
ER -

References

top
  1. T. Crespo, Z. Hajto, Finite linear groups as differential Galois groups, Bull. Pol. Ac. Math 49 (2001), 363-375 Zbl1040.12009MR1872670
  2. T. Crespo, Z. Hajto, Primitive unimodular groups of degree 2 as differential Galois groups, J. of Algebra 229 (2000), 678-694 Zbl1002.12005MR1769295
  3. T. Crespo, Z. Hajto, Recouvrements doubles comme groupes de Galois différentiels, C.R. Acad. Sci. Paris, Série I 333 (2001), 271-274 Zbl1018.12005MR1854763
  4. I. Kaplansky, An introduction to differential algebra, (1976), Hermann Zbl0083.03301MR460303
  5. A.R. Magid, Lectures on differential Galois theory, A.M.S (1997) Zbl0855.12001
  6. G. Malle, B.H. Matzat, Inverse Galois Theory, (1999), Springer-Verlag, Berlin Zbl0940.12001MR1711577
  7. G.A. Miller, H.F. Blichfeldt, L.E. Dickson, Theory and applications of finite groups, (1916), John Wiley and sons, Inc. Zbl46.0171.02
  8. J-P. Serre, L’invariant de Witt de la forme Tr ( x 2 ) , Comment. Math. Helvetici 59 (1984), 651-676 Zbl0565.12014MR780081
  9. J-P. Serre, Cohomologie galoisienne, (1994), Springer Verlag Zbl0812.12002MR1324577
  10. M.F. Singer, An outline of differential Galois theory, Computer Algebra and Differential Equations (1989), 3-57, Academic Press Zbl0713.12005
  11. M.F. Singer, F. Ulmer, Galois groups of second and third order linear differential equations, Journal of Symbolic Computation 16 (1993), 9-36 Zbl0802.12004MR1237348

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.