eprintid: 8278
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/82/78
datestamp: 2008-05-29 13:25:25
lastmod: 2015-04-23 21:15:34
status_changed: 2012-08-14 15:25:28
type: preprint
metadata_visibility: show
creators_name: Hardouin, Charlotte
title: Iterative $q$-Difference Galois Theory
ispublished: pub
subjects: ddc-510
divisions: i-708000
cterms_swd: $q$-difference Galois theory
cterms_swd: roots of unity
cterms_swd: iterative operators
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.
abstract_translated_lang: eng
date: 2008
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00008278
portal_cluster_id: p-iwrpp
portal_order: 08278
ppn_swb: 1646787935
own_urn: urn:nbn:de:bsz:16-opus-82789
language: eng
bibsort: HARDOUINCHITERATIVEQ2008
full_text_status: public
series: IWR-Preprints
citation:   Hardouin, Charlotte  (2008) Iterative $q$-Difference Galois Theory.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/8278/1/itaut7.pdf