El Kaoutit, Laiachi; Gómez-Torrecillas, José On the finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory. (English) Zbl 1482.12004 Bull. Belg. Math. Soc. - Simon Stevin 28, No. 1, 53-121 (2021). Picard-Vessio’s theory of differential field extensions, developed by Kolchin (see [M. van der Put and M. F. Singer, Galois theory of linear differential equations. Berlin: Springer (2003; Zbl 1036.12008)]), had a major influence on theory of linear differential equations. It stimulated the emergence of new ideas enriching this theory (see [A. Ovchinnikov, Transform. Groups 14, No. 1, 195–223 (2009; Zbl 1229.18008)]). This paper presents such an idea. In it, the authors give “a Hopf algebroid approach to the Picard-Vessiot theory of linear differential matrix equations with coefficients in the polynomial complex algebra.” Reviewer: Mykola Grygorenko (Kyïv) Cited in 5 Documents MSC: 12H20 Abstract differential equations 16T05 Hopf algebras and their applications 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16D90 Module categories in associative algebras 16T10 Bialgebras 58H05 Pseudogroups and differentiable groupoids 13N15 Derivations and commutative rings 12H05 Differential algebra 13N05 Modules of differentials Keywords:differential Galois groupoid; differential modules; Hopf algebroids; Lie algebroids; linear differential equations; Picard-Vessiot extension of differential rings; rings of differential operators; Tannaka reconstruction Citations:Zbl 1036.12008; Zbl 1229.18008 PDFBibTeX XMLCite \textit{L. El Kaoutit} and \textit{J. Gómez-Torrecillas}, Bull. Belg. Math. 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