Differential Galois Theory and Lie-Vessiot Systems (Paperback) (ISBN-13: 9783639096019)

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.

Author: David Blázquez-Sanz
ISBN-10: 3639096010
ISBN-13: 9783639096019
Publisher: VDM Verlag Dr. Mueller E.K.
Language: English
Published: 10/29/2008
Pages: 192
Format: Paperback
Weight: 0.58lbs
Size: 9.00h x 6.00w x 0.41d