# Picard-Vessiot theory in general Galois theory

Banach Center Publications (2011)

- Volume: 94, Issue: 1, page 263-293
- ISSN: 0137-6934

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topHiroshi 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 -

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