Solution of the Inverse Problem of Differential Galois Theory in the Classical Case

DOI10.2307/2374143zbMath0423.12021OpenAlexW2316858811MaRDI QIDQ3856861

Carol Tretkoff, Marvin D. Tretkoff

Publication date: 1979

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374143

zbMATH Keywords

Picard-Vessiot extensiondifferential fieldinverse problem of Galois theory of differential fieldsrealization of groups as Galois group

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Differential algebra (12H05)

Related Items (20)

Nonintegrability of the classical Zeeman Hamiltonian ⋮ Necessary conditions for Liouvillian solutions of (third order) linear differential equations ⋮ Linear algebraic groups as parameterized Picard-Vessiot Galois groups ⋮ Degree bound for toric envelope of a linear algebraic group ⋮ Unipotent differential algebraic groups as parameterized differential Galois groups ⋮ The differential Galois group of the rational function field ⋮ Differential and difference algebra ⋮ On Ramis's solution of the local inverse problem of differential Galois theory ⋮ Group-theoretic obstructions to integrability ⋮ Solvable-by-finite groups as differential Galois groups ⋮ Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations ⋮ Galois theory of differential equations, algebraic groups and Lie algebras ⋮ Algebraic groups as difference Galois groups of linear differential equations ⋮ Differential embedding problems over complex function fields ⋮ Unnamed Item ⋮ On the generalized Riemann--Hilbert problem with irregular singularities ⋮ Differential Galois groups over Laurent series fields ⋮ Free differential Galois groups ⋮ The holonomy group at infinity of the Painlevé VI equation ⋮ Formal solutions of differential equations

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