Differential Galois Theory and Lie Symmetries

作者：Blazquez Sanz David^*; Morales Ruiz Juan J; Weil Jacques Arthur

来源：Symmetry Integrability and Geometry-Methods and Applications, 2015, 11: 092.

DOI：10.3842/SIGMA.2015.092

• linear differential system
• Picard-Vessiot theory
• differential Galois theory
• infinitesimal symmetries

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.

• 出版日期2015