Blázquez-Sanz David: Differential Galois Theory and Lie-Vess
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- Englisch ausgewählt
68,00 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Verlag
VDMSeitenzahl
192
Maße (L/B/H)
22/15/1,2 cm
Gewicht
302 g
Sprache
Englisch
ISBN
978-3-639-09601-9
The purpose of this work is to develop a differential
Galois theory for differential equations admitting
superposition laws. First, we characterize those
differential equations in terms of Lie group actions,
generalizing some classical results due to S. Lie. We
call them Lie-Vessiot systems. Then, we develop a
differential Galois theory for Lie-Vessiot systems
both in the complex analytic and algebraic contexts.
In the complex analytic context we give a theory that
generalizes the tannakian approach to the classical
Picard-Vessiot theory. In the algebraic case, we
study differential equations under the formalism of
differential algebra. We prove that algebraic
Lie-Vessiot systems are solvable in strongly normal
extensions. Therefore, Lie-Vessiot systems are
differential equations attached to the Kolchin''s
differential Galois theory.
Galois theory for differential equations admitting
superposition laws. First, we characterize those
differential equations in terms of Lie group actions,
generalizing some classical results due to S. Lie. We
call them Lie-Vessiot systems. Then, we develop a
differential Galois theory for Lie-Vessiot systems
both in the complex analytic and algebraic contexts.
In the complex analytic context we give a theory that
generalizes the tannakian approach to the classical
Picard-Vessiot theory. In the algebraic case, we
study differential equations under the formalism of
differential algebra. We prove that algebraic
Lie-Vessiot systems are solvable in strongly normal
extensions. Therefore, Lie-Vessiot systems are
differential equations attached to the Kolchin''s
differential Galois theory.
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