Diff\\érentielles non commutatives et th\\éorie de Galois diff\\érentielle ou aux diff\\érences

Yves André (1)

1 IMJ - Institut de Mathématiques de Jussieu

We show how the Galois-Picard_Vessiot theory of differential equations and difference equations, and the theory of holonomy groups in differential geometry, are different aspects of a unique Galois theory. The latter is based upon the construction and study of the tensor product of non commutative connections over a commutative base, without any curvature assumption. This theory provides an algebraic frame for the study of the confluence arising when the increment of a difference equation tends to 0.

Domaines: Mathématiques générales [math.GM]; Algèbres quantiques [math.QA]; Algèbre commutative [math.AC]

Yves André. Diff\\érentielles non commutatives et th\\éorie de Galois diff\\érentielle ou aux diff\\érences. Annales Scientifiques de l'École Normale Supérieure, 2001, 34, pp.685-739. ⟨hal-00010032⟩