Galois Theory, Differential Equations, and Lie Groups?

["pi"mp]

I apologize for the informal and un-rigourous question. I have heard, in passing, that doing Galois Theory over Lie Groups instead of discrete groups is connected to solutions of differential equations instead of algebraic equations.

First of all, is this correct? If so, what is this correspondence called and where can I learn about it?
Much thanks!

 

[Boorglar]

I think the term you are looking for is Differential Galois Theory.
Don't ask me how it works, because I only know a bit of the "normal" Galois Theory (over finite field extensions), and I don't know how it's being used here.

http://en.wikipedia.org/wiki/Differential_Galois_theory

The article also mentions Picard-Vessiot theory, which seems to deal with solutions of differential equations in terms of integrals.