Absolute reducibility of differential operators and Galois groups
type: Item
instance of: scholarly article
title: Absolute reducibility of differential operators and Galois groups
zbMATH Open document ID: 1084.12003
published in: Journal of Algebra
publication date: 2004-10-04T00:00:00Z
review text: A linear differential operator \(L\) over \(C(x)\) is called absolutely reducible if it admits a factorization over an algebraic extension of \(C(x)\) (equivalently: if the connected component of identity of the Galois group of \(L\) acts reducibly on the space of solutions of \(L\)).The problem of absolute factorization of the operator has an important applied value [see Mat. Zametki 34, No. 4, 481--484 (1983; Zbl 0548.12014)]. Existing methods [see J. Symb. Comput. 28, No. 4-5, 473--494 (1999; Zbl 0997.12009)] of such factorization are very complex and ineffective. The authors offer a more effective approach for the decision of this problem. They give sharp bounds on the degree of the extension that is needed in order to compute an absolute factorization.
Mathematics Subject Classification ID: 12H05
zbMATH DE Number: 2105789
zbMATH Keywords: linear differential operator
zbMATH Keywords: differential Galois group
author: Elie Compoint
author: Jacques-Arthur Weil
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.11.010
OpenAlex ID: W2053447949
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DOI: 10.1016/J.JALGEBRA.2003.11.010
description: scientific article; zbMATH DE number 2105789