On the Constructive Inverse Problem in Differential Galois Theory

2004/03/23 by William J. Cook, Cook, William J., Claude Mitschi +3
Computer Science · Mathematics · #Polynomial and algebraic computation #math.CA #math.GM #math.GR #msc:12H05 #msc:12H20 #msc:34M50

paper · pdf · doi:10.48550/arxiv.math/0403378

Several misprints have been corrected and the statement of Propositions 3.2 and 3.4 have been made more precise and their proofs expanded

arxiv created 2005/06/05 · arxiv updated 2009/12/01

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.

Related

• The regular singular inverse problem in differential Galois theory
• Algebraic groups as difference Galois groups of linear differential equations
• A note on the inverse problem for finite differential Galois groups
• Root Parametrized Differential Equations for the classical groups
• Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups