On a general difference Galois theory I

Shuji Morikawa[1]

  • [1] Nagoya University Graduate School of Mathematics Nagoya (Japan)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 7, page 2709-2732
  • ISSN: 0373-0956

Abstract

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We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic 0 , we attach its Galois group, which is a group of coordinate transformation.

How to cite

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Morikawa, Shuji. "On a general difference Galois theory I." Annales de l’institut Fourier 59.7 (2009): 2709-2732. <http://eudml.org/doc/10469>.

@article{Morikawa2009,
abstract = {We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic $0$, we attach its Galois group, which is a group of coordinate transformation.},
affiliation = {Nagoya University Graduate School of Mathematics Nagoya (Japan)},
author = {Morikawa, Shuji},
journal = {Annales de l’institut Fourier},
keywords = {General difference Galois theory; dynamical system; integrable dynamical system; Galois groupoid; difference equations; Galois theory; infinite-dimensional Lie algebras},
language = {eng},
number = {7},
pages = {2709-2732},
publisher = {Association des Annales de l’institut Fourier},
title = {On a general difference Galois theory I},
url = {http://eudml.org/doc/10469},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Morikawa, Shuji
TI - On a general difference Galois theory I
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 7
SP - 2709
EP - 2732
AB - We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic $0$, we attach its Galois group, which is a group of coordinate transformation.
LA - eng
KW - General difference Galois theory; dynamical system; integrable dynamical system; Galois groupoid; difference equations; Galois theory; infinite-dimensional Lie algebras
UR - http://eudml.org/doc/10469
ER -

References

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  1. G. Casale, Sur le groupoïde de Galois d’un feuilletage, (2004), Toulouse 
  2. G. Casale, Enveloppe galoisienne d’une application rationnelle de ℙ 1 , Publ. Mat. 50 (2006), 191-202 Zbl1137.37022MR2325017
  3. Charles H. Franke, Picard-Vessiot theory of linear homogeneous difference equations, Trans. Amer. Math. Soc. 108 (1963), 491-515 Zbl0116.02604MR155819
  4. A. Granier, Un D -groupoïde de Galois pour les équations au q -différences, (2009), Toulouse 
  5. Charlotte Hardouin, Michael F. Singer, Differential Galois theory of linear difference equations, Math. Ann. 342 (2008), 333-377 Zbl1163.12002MR2425146
  6. F. Heiderlich, Infinitesimal Galois theory for D -module fields 
  7. B. Malgrange, Le groupoïde de Galois d’un feuilletage, Essays on geometry and related topics, Vol. 1, 2 38 (2001), 465-501, Enseignement Math., Geneva Zbl1033.32020MR1929336
  8. S. Morikawa, H Umemura, On a general Galois theory of difference equations II, Ann. Inst. Fourier 59 (2009), 2733-2771 Zbl1194.12006
  9. Marius van der Put, Michael F. Singer, Galois theory of difference equations, 1666 (1997), Springer-Verlag, Berlin Zbl0930.12006MR1480919
  10. Hiroshi Umemura, Differential Galois theory of infinite dimension, Nagoya Math. J. 144 (1996), 59-135 Zbl0878.12002MR1425592
  11. Hiroshi Umemura, Galois theory of algebraic and differential equations, Nagoya Math. J. 144 (1996), 1-58 Zbl0885.12004MR1425591
  12. Hiroshi Umemura, Galois theory and Painlevé equations, Théories asymptotiques et équations de Painlevé 14 (2006), 299-339, Soc. Math. France, Paris Zbl1156.34080MR2353471
  13. Hiroshi Umemura, Invitation to Galois theory, Differential equations and quantum groups 9 (2007), 269-289, Eur. Math. Soc., Zürich MR2322334

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