Differential Galois Theory and Lie Symmetries

[摘要] 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.

[关键词] linear dif ferential system;Picard–Vessiot theory;dif ferential Galois theory;infinitesimal symmetries