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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 054, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.054 (Mi sigma1591) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Reduced Forms of Linear Differential Systems and the Intrinsic Galois–Lie Algebra of Katz

Moulay Barkatoua, Thomas Cluzeaua, Lucia Di Viziob, Jacques-Arthur Weila

a XLIM, UMR7252, Université de Limoges et CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France
b Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France
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DOI: https://doi.org/10.3842/SIGMA.2020.054
Abstract: Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504–1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if any differential module in an algebraic construction admits a constant basis. Then we derive an explicit version of this statement. We finally deduce some properties of the Lie algebra of Katz's intrinsic Galois group.
Keywords: linear differential systems, differential Galois theory, Lie algebras, reduced forms.
Received: January 20, 2020; in final form June 4, 2020; Published online June 17, 2020
Bibliographic databases:
Document Type: Article
MSC: 34M03, 34M15, 34C20
Language: English
Citation: Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio, Jacques-Arthur Weil, “Reduced Forms of Linear Differential Systems and the Intrinsic Galois–Lie Algebra of Katz”, SIGMA, 16 (2020), 054, 13 pp.
Citation in format AMSBIB
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