On the Constructive Inverse Problem in Differential Galois Theory
General Mathematics
2007-05-23 v3 Classical Analysis and ODEs
Group Theory
Abstract
We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a product of groups of type An, Cn, Dn, E6, or E7, we construct a differential equation over C(x) having Galois group G.
Cite
@article{arxiv.math/0403378,
title = {On the Constructive Inverse Problem in Differential Galois Theory},
author = {William J. Cook and Claude Mitschi and Michael F. Singer},
journal= {arXiv preprint arXiv:math/0403378},
year = {2007}
}
Comments
Several misprints have been corrected and the statement of Propositions 3.2 and 3.4 have been made more precise and their proofs expanded