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arXiv · 1912.10567

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

Moulay Barkatou·Thomas Cluzeau·Lucia Di Vizio·Jacques-Arthur Weil
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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.

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Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio, Jacques-Arthur Weil. 2019-12-23. Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz. https://doi.org/10.3842/sigma.2020.054

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