Linear algebraic groups as parameterized Picard-Vessiot Galois groups

被引：14

作者：

Singer, Michael F. ^{[1
]}

机构：

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

来源：

JOURNAL OF ALGEBRA | 2013年 / 373卷

基金：

美国国家科学基金会;

关键词：

Parameterized Picard-Vessiot theory; Linear algebraic groups; Inverse problem; INVERSE PROBLEM;

D O I：

10.1016/j.jalgebra.2012.09.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x' = 1, for certain differential fields k, if and only if its identity component has no one-dimensional quotient as a linear algebraic group. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：153 / 161

页数：9

共 50 条

[1] Picard-Vessiot extensions, linear differential algebraic groups, and their torsors
Meretzky, David
Pillay, Anand
[J]. COMMUNICATIONS IN ALGEBRA, 2024,
[2] The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups
Pillay, Anand
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (06): : 809 - 817
[3] Differential Galois cohomology and parameterized Picard-Vessiot extensions
Sanchez, Omar Leon
Pillay, Anand
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2021, 23 (08)
[4] ALGEBRAIC MATRIC GROUPS AND THE PICARD-VESSIOT THEORY OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS
KOLCHIN, ER
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1946, 52 (11) : 1003 - 1004
[5] ALGEBRAIC MATRIC GROUPS AND THE PICARD-VESSIOT THEORY OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS
KOLCHIN, ER
[J]. ANNALS OF MATHEMATICS, 1948, 49 (01) : 1 - 42
[6] GENERIC PICARD-VESSIOT EXTENSIONS FOR NONCONNECTED GROUPS
Juan, Lourdes
Ledet, Arne
[J]. COMMUNICATIONS IN ALGEBRA, 2016, 44 (07) : 2989 - 3004
[7] Galois Correspondence Theorem for Picard-Vessiot Extensions
Crespo T.
Hajto Z.
Sowa-Adamus E.
[J]. Arnold Mathematical Journal, 2016, 2 (1) : 21 - 27
[8] Some applications of parameterized Picard-Vessiot theory
Mitschi, C.
[J]. IZVESTIYA MATHEMATICS, 2016, 80 (01) : 167 - 188
[9] Parameterized Picard-Vessiot extensions and Atiyah extensions
Gillet, Henri
Gorchinskiy, Sergey
Ovchinnikov, Alexey
[J]. ADVANCES IN MATHEMATICS, 2013, 238 : 322 - 411
[10] PICARD-VESSIOT EXTENSIONS WITH SPECIFIED GALOIS GROUP
Chinburg, Ted
Juan, Lourdes
Magid, Andy R.
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2009, 243 (02) : 233 - 242

← 1 2 3 4 5 →