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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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A Galois D -groupoid for q -difference equations

A Galois $D$ -groupoid for $q$ -difference equations