A Galois D -groupoid for q -difference equations

Anne Granier[1]

  • [1] Ruprecht-Karls-Universität Heidelberg Mathematics Center of Heidelberg (MATCH) & Interdisciplinary Center for Scientific Computing (IWR) Im Neuenheimer Feld 368 69120 Heidelberg (Germany)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 4, page 1493-1516
  • ISSN: 0373-0956

Abstract

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We first recall Malgrange’s definition of D -groupoid and we define a Galois D -groupoid for q -difference equations. Then, we compute explicitly the Galois D -groupoid of a constant linear q -difference system, and show that it corresponds to the q -difference Galois group. Finally, we establish a conjugation between the Galois D -groupoids of two equivalent constant linear q -difference systems, and define a local Galois D -groupoid for Fuchsian linear q -difference systems by giving its realizations.

How to cite

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Granier, Anne. "A Galois $D$-groupoid for $q$-difference equations." Annales de l’institut Fourier 61.4 (2011): 1493-1516. <http://eudml.org/doc/219704>.

@article{Granier2011,
abstract = {We first recall Malgrange’s definition of $D$-groupoid and we define a Galois $D$-groupoid for $q$-difference equations. Then, we compute explicitly the Galois $D$-groupoid of a constant linear $q$-difference system, and show that it corresponds to the $q$-difference Galois group. Finally, we establish a conjugation between the Galois $D$-groupoids of two equivalent constant linear $q$-difference systems, and define a local Galois $D$-groupoid for Fuchsian linear $q$-difference systems by giving its realizations.},
affiliation = {Ruprecht-Karls-Universität Heidelberg Mathematics Center of Heidelberg (MATCH) & Interdisciplinary Center for Scientific Computing (IWR) Im Neuenheimer Feld 368 69120 Heidelberg (Germany)},
author = {Granier, Anne},
journal = {Annales de l’institut Fourier},
keywords = {Malgrange’s $D$-groupoids; $q$-difference equations; $q$-difference Galois groups; Malgrange’s -groupoids; -difference equations; -difference Galois groups; Fuchsian linear -difference systems},
language = {eng},
number = {4},
pages = {1493-1516},
publisher = {Association des Annales de l’institut Fourier},
title = {A Galois $D$-groupoid for $q$-difference equations},
url = {http://eudml.org/doc/219704},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Granier, Anne
TI - A Galois $D$-groupoid for $q$-difference equations
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1493
EP - 1516
AB - We first recall Malgrange’s definition of $D$-groupoid and we define a Galois $D$-groupoid for $q$-difference equations. Then, we compute explicitly the Galois $D$-groupoid of a constant linear $q$-difference system, and show that it corresponds to the $q$-difference Galois group. Finally, we establish a conjugation between the Galois $D$-groupoids of two equivalent constant linear $q$-difference systems, and define a local Galois $D$-groupoid for Fuchsian linear $q$-difference systems by giving its realizations.
LA - eng
KW - Malgrange’s $D$-groupoids; $q$-difference equations; $q$-difference Galois groups; Malgrange’s -groupoids; -difference equations; -difference Galois groups; Fuchsian linear -difference systems
UR - http://eudml.org/doc/219704
ER -

References

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