Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz

DOI10.3842/SIGMA.2020.054zbMath1448.12002arXiv1912.10567MaRDI QIDQ2190680

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

Publication date: 21 June 2020

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10567

zbMATH Keywords

Galois cohomologyLie algebrasdifferential Galois theorylinear differential systemsreduced forms

Mathematics Subject Classification ID

Galois cohomology (12G05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Differential algebra (12H05) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items

Solutions of algebraic linear ordinary differential equations, Darboux transformations for orthogonal differential systems and differential Galois theory, Differential Galois Theory and Integration

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An algorithm for solving second order linear homogeneous differential equations
• Galois groups of second and third order linear differential equations
• Liouvillian solutions of linear differential equations of order three and higher
• Computing Galois groups of completely reducible differential equations
• Computing the Lie algebra of the differential Galois group: the reducible case
• Solving linear differential equations
• Hrushovski's algorithm for computing the Galois group of a linear differential equation
• A characterization of reduced forms of linear differential systems
• Around the numeric-symbolic computation of differential Galois groups
• Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System
• Contribution to the Picard-Vessiot Theory of Homogeneous Linear Differential Equations
• Decomposing a 4th order linear differential equation as a symmetric product
• Computing the Galois group of a linear differential equation
• A conjecture in the arithmetic theory of differential equations
• Degree bound for toric envelope of a linear algebraic group
• A Symplectic Kovacic's Algorithm in Dimension 4
• On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
• Some Basic Theorems in Differential Algebra (Characteristic p, Arbitrary)
• Computing the Galois group of a linear differential equation of order four.