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

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.

References in corpus (1)

• Computing the Lie algebra of the differential Galois group: the reducible case

Cited by in corpus (2)

• Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
• The art of algorithmic guessing in $\text{gfun}$