Abstract
Picard-Vessiot extensions are determined by their differential module structure. For a fixed group G, Picard-Vessiot extensions with differential Galois group G are all isomorphic as G-modules but not as differential rings. We show that isomorphism classes of Picard-Vessiot extensions with group G correspond to G-orbits in a certain finite-dimensional vector space with G-action.
Original language | English |
---|---|
Pages (from-to) | 233-242 |
Number of pages | 10 |
Journal | Pacific Journal of Mathematics |
Volume | 243 |
Issue number | 2 |
DOIs | |
State | Published - Dec 2009 |
Keywords
- Differential
- Galois
- Picard-Vessiot