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On the finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory. (English) Zbl 1482.12004

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.”

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
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References:

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