On the constructive inverse problem in differential Galois theory

被引：2

作者：

Cook, WJ

Mitschi, C

Singer, MF

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Univ Strasbourg, Inst Rech Math Avancee, Strasbourg, France

[3] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2005年 / 33卷 / 10期

基金：

美国国家科学基金会;

关键词：

Galois theory; inverse problem; linear differential equations; Picard-Vessiot;

D O I：

10.1080/00927870500243304

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G(0) = G(1) - - - - - G(r), where each G(i) is a simple group of type A(l), C-l, D-l, E-6, or E-7, we construct a differential equation over C(x) having Galois group G.

引用

页码：3639 / 3665

页数：27

共 50 条

[41] DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY
Maciejewski, Andrzej J.
Przybylska, Maria
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2009, 6 (08) : 1357 - 1390
[42] ON THE GALOIS THEORY OF DIFFERENTIAL FIELDS
KOLCHIN, ER
AMERICAN JOURNAL OF MATHEMATICS, 1955, 77 (04) : 868 - 894
[43] Generalized differential Galois theory
Landesman, Peter
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (08) : 4441 - 4495
[44] ON NONLINEAR DIFFERENTIAL GALOIS THEORY
Ｂ．ＭＡＬＧＲＡＮＧＥ
ChineseAnnalsofMathematics, 2002, (02) : 219 - 226
[45] General Differential Galois Theory
Trushin, D. V.
MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2010, 65 (03) : 123 - 123
[46] AN EXTENSION OF DIFFERENTIAL GALOIS THEORY
KREIMER, HF
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 118 (06) : 247 - &
[47] Differential Galois theory II
Pillay, A
ANNALS OF PURE AND APPLIED LOGIC, 1997, 88 (2-3) : 181 - 191
[48] Differential Galois theory I
Pillay, A
ILLINOIS JOURNAL OF MATHEMATICS, 1998, 42 (04) : 678 - 699
[49] On nonlinear differential Galois theory
Malgrange, B
CHINESE ANNALS OF MATHEMATICS SERIES B, 2002, 23 (02) : 219 - 226
[50] Tame torsion and the tame inverse Galois problem
Matthew Bisatt
Tim Dokchitser
Mathematische Annalen, 2021, 381 : 1439 - 1453

← 1 2 3 4 5 →