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

Symmetry Integrability and Geometry-Methods and Applications

article

Moulay Barkatou¹  Thomas Cluzeau¹  Lucia Di Vizio²  Jacques-Arthur Weil¹ 

[1] Université de Limoges et CNRS;Université Paris-Saclay, Laboratoire de mathématiques de Versailles

关键词: linear differential systems;    differential Galois theory;    Lie algebras;    reduced forms;   

DOI  :  10.3842/SIGMA.2020.054

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown