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Differential Galois Theory and Lie Symmetries
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: linear differential system; Picard–Vessiot theory; differential Galois theory; infinitesimal symmetries. 
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}
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David Blázquez-Sanz; Juan J. Morales-Ruiz; Jacques-Arthur Weil. Differential Galois Theory and Lie Symmetries. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a91/

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