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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 092, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.092 (Mi sigma1073) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Galois Theory and Lie Symmetries

David Blázquez-Sanza, Juan J. Morales-Ruizb, Jacques-Arthur Weilc

a Universidad Nacional de Colombia, Colombia
b Universidad Politécnica de Madrid, Spain
c Université de Limoges, France
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DOI: https://doi.org/10.3842/SIGMA.2015.092
Abstract: 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.
Received: March 31, 2015; in final form November 11, 2015; Published online November 20, 2015
Bibliographic databases:
Document Type: Article
MSC: 12H05; 34M15; 34A26
Language: English
Citation: David Blázquez-Sanz, Juan J. Morales-Ruiz, Jacques-Arthur Weil, “Differential Galois Theory and Lie Symmetries”, SIGMA, 11 (2015), 092, 17 pp.
Citation in format AMSBIB
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