Galois groups and connection matrices of $q$-difference equations
Author:
Pavel I. Etingof
Journal:
Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 1-9
MSC (1991):
Primary 12H10, 39A10
DOI:
https://doi.org/10.1090/S1079-6762-95-01001-8
MathSciNet review:
1336694
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Abstract: 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.
- Richard M. Cohn, Difference algebra, Interscience Publishers John Wiley & Sons, New York-London-Sydeny, 1965. MR 0205987
- P. Deligne, Catégories tannakiennes, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 111–195 (French). MR 1106898
- Charles H. Franke, Picard-Vessiot theory of linear homogeneous difference equations, Trans. Amer. Math. Soc. 108 (1963), 491–515. MR 155819, DOI https://doi.org/10.1090/S0002-9947-1963-0155819-3
- Irving Kaplansky, An introduction to differential algebra, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1251, Hermann, Paris, 1957. Publ. Inst. Math. Univ. Nancago, No. 5. MR 0093654
- E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York-London, 1973. Pure and Applied Mathematics, Vol. 54. MR 0568864
Ritt, J.F., Differential algebra, vol. XXXIII, Colloquium publ. of AMS, 1950.
Cohn, R.M., Difference algebra, Interscience Publ., New York, 1965.
Deligne P., Catégories Tannakiennes, Grothendieck Festschrift 2 (1991), Birkhäuser, Boston, 111-195.
Franke, C.H., Picard-Vessiot theory of linear homogeneous difference equations, Trans. of AMS 108 (1963), 491-515.
Kaplansky, I., An introduction to differential algebra, Hermann, Paris, 1957.
Kolchin, E.R., Differential algebra and algebraic groups, Acad. Press, New York, 1973.
Ritt, J.F., Differential algebra, vol. XXXIII, Colloquium publ. of AMS, 1950.
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Pavel I. Etingof
Affiliation:
address Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.
Email:
etingof@math.harvard.edu
Received by editor(s):
April 6, 1995
Communicated by:
David Kazhdan
Article copyright:
© Copyright 1995
American Mathematical Society
