Galois theory of parameterized differential equations and linear differential algebraic groups

DOI10.4171/020-1/7zbMath1356.12004OpenAlexW4246681111MaRDI QIDQ5892289

Michael F. Singer, Phyllis Joan Cassidy

Publication date: 17 February 2017

Published in: Differential Equations and Quantum Groups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/020-1/7

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Differential algebra (12H05) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items

Differential Tannakian categories, The Malgrange-Galois groupoid of the Painlevé VI equation with parameters, Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence, The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups, Parameterized Picard-Vessiot extensions and Atiyah extensions, Generalized Picard-Vessiot extensions and differential Galois cohomology, Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation, Galois groups of linear difference-differential equations, New classes of parameterized differential Galois groups, A Galois-theoretic proof of the differential transcendence of the incomplete gamma function, Isomonodromic differential equations and differential categories, Difference Galois groups under specialization, Almost-simple affine difference algebraic groups, Zariski closures of reductive linear differential algebraic groups, Triviality of differential Galois cohomology of linear differential algebraic groups, Hypertranscendence and linear difference equations, Differential Galois cohomology and parameterized Picard–Vessiot extensions, A categorical approach to Picard-Vessiot theory, Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators