%0 Generic
%A Hartmann, Julia
%D 2002
%F heidok:3085
%K DifferentialgaloistheorieDifferential Galois theory
%R 10.11588/heidok.00003085
%T On the Inverse Problem in Differential Galois Theory
%U https://archiv.ub.uni-heidelberg.de/volltextserver/3085/
%X Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the base field and commute with the derivation. Differential Galois groups are linear algebraic groups over the field of constants of the base field. In analogy to the classical situation, one considers the inverse problem: Which linear algebraic groups occur as differential Galois groups over a given differential field? The main result of this thesis is the following theorem: Every linear algebraic group defined over the algebraically closed field K occurs as the differential Galois group of some Picard-Vessiot extension of K(t) with derivation d/dt.