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A Galois D -groupoid for q -difference equations

Anne Granier — 2011

Annales de l’institut Fourier

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.

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