Directly to content
  1. Publishing |
  2. Search |
  3. Browse |
  4. Recent items rss |
  5. Open Access |
  6. Jur. Issues |
  7. DeutschClear Cookie - decide language by browser settings

Iterative $q$-Difference Galois Theory

Hardouin, Charlotte

[img]
Preview
PDF, English Print-on-Demand-Kopie (epubli)
Download (330Kb) | Lizenz: Print on Demand

Citation of documents: Please do not cite the URL that is displayed in your browser location input, instead use the persistent URL or the URN below, as we can guarantee their long-time accessibility.

Abstract

Initially, the Galois theory of $q$-difference equations was built for $q$ unequal to a root of unity. This choice was made in order to avoid the increase of the field of constants to a transcendental field. Inspired by the work of B.H. Matzat and M. van der Put, we consider in this paper a family of iterative difference operators instead of considering just one difference operator, and in this way we stop the increase of the constant field and succeed in setting up a Picard-Vessiot theory for $q$-difference equations where $q$ is a root of unity that extend the Galois theory of difference equations of Singer and van der Put. The theory we obtain is quite the exact translation of the iterative differential Galois theory developed by B.H. Matzat and M. van der Put to the $q$-difference world.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 29 May 2008 13:25
Date: 2008
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: $q$-difference Galois theory, roots of unity, iterative operators
About | FAQ | Contact | Imprint |
OA-LogoLogo der Open-Archives-Initiative