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Hopf algebraic approach to Picard-Vessiot theory. (English) Zbl 1218.12003
Hazewinkel, M. (ed.), Handbook of algebra. Volume 6. Amsterdam: Elsevier/North-Holland (ISBN 978-0-444-53257-2/hbk). Handbook of Algebra 6, 127-171 (2009).
Picard-Vessiot (PV) theory is a Galois theory of linear differential equations. In this survey article the authors present their Hopf-algebraic approach to this theory. They discuss the PV theory in the differential context, \(C\)-ferential context (\(C\) a cocommutative coalgebra) and the unified PV theory.
For the entire collection see [Zbl 1182.00007].

MSC:
12H20 Abstract differential equations
12-02 Research exposition (monographs, survey articles) pertaining to field theory
16T05 Hopf algebras and their applications
12H05 Differential algebra
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