Geodesic
Galois groups and connection matrices of 𝑞-difference equations
Etingof, Pavel1
1 address Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 1, pp. 1-9.

Voir la notice de l'article provenant de la source American Mathematical Society

We study the Galois group of a matrix $q$-difference equation with rational coefficients which is regular at $0$ and $\infty$, in the sense of (difference) Picard-Vessiot theory, and show that it coincides with the algebraic group generated by matrices $C(u)C(w)^{-1}$ $u,w\in \mathbb {C}^*$, where $C(z)$ is the Birkhoff connection matrix of the equation.
DOI : 10.1090/S1079-6762-95-01001-8

Etingof, Pavel 1

1 address Department of Mathematics, Harvard University, Cambridge, MA 02138, USA. 
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Etingof, Pavel. Galois groups and connection matrices of 𝑞-difference equations. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 1, pp. 1-9. doi : 10.1090/S1079-6762-95-01001-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-01001-8/

[1] Cohn, Richard M. Difference algebra 1965

[2] Deligne, P. Catégories tannakiennes 1990 111 195

[3] Franke, Charles H. Picard-Vessiot theory of linear homogeneous difference equations Trans. Amer. Math. Soc. 1963 491 515

[4] Kaplansky, Irving An introduction to differential algebra 1957 63

[5] Kolchin, E. R. Differential algebra and algebraic groups 1973

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