Picard-Vessiot extensions are determined by their dieren- tial module structure. For a xed group G Picard-Vessiot extensions with dierential Galois group G are all isomorphic as G-modules but not as dierential rings. It is then shown that isomorphism classes of Picard-Vessiot extensions with group G correspond to G-orbits in a cer- tain nite dimensional vector space with G-action.
|Journal||Pacific Journal of Mathematics|
|State||Published - Dec 2009|