Picard-Vessiot theory in general Galois theory

Hiroshi Umemura. "Picard-Vessiot theory in general Galois theory." Banach Center Publications 94.1 (2011): 263-293. <http://eudml.org/doc/281874>.

@article{HiroshiUmemura2011,
abstract = {We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory. We apply the proof to iterative q-difference Picard-Vessiot theory to show that Picard-Vessiot theory for iterative q-difference field extensions is in the scope of the general Galois theory of Heiderich. We also show that Picard-Vessiot theory is commutative in the sense that studying linear difference-differential equations, no matter how twisted the operators are, we cannot encounter quantification of the Galois groupoid.},
author = {Hiroshi Umemura},
journal = {Banach Center Publications},
keywords = {Picard-Vessiot theory; general difference-differential Galois theory; iterative q-difference theory},
language = {eng},
number = {1},
pages = {263-293},
title = {Picard-Vessiot theory in general Galois theory},
url = {http://eudml.org/doc/281874},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Hiroshi Umemura
TI - Picard-Vessiot theory in general Galois theory
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 263
EP - 293
AB - We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory. We apply the proof to iterative q-difference Picard-Vessiot theory to show that Picard-Vessiot theory for iterative q-difference field extensions is in the scope of the general Galois theory of Heiderich. We also show that Picard-Vessiot theory is commutative in the sense that studying linear difference-differential equations, no matter how twisted the operators are, we cannot encounter quantification of the Galois groupoid.
LA - eng
KW - Picard-Vessiot theory; general difference-differential Galois theory; iterative q-difference theory
UR - http://eudml.org/doc/281874
ER -