Differential Galois theory and Lie symmetries

David Blázquez-Sanz, Juan José Morales-Ruiz, Jacques-Arthur Weil

Published 2015-03-31Version 1

We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the differential Galois group in the system in a way that depends of the Maclaurin series of the symmetry along the zero solution.