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
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Cite this
Chinburg, T., Juan, L., & Magid, A. R. (2009). Picard-Vessiot extensions with specified Galois group. Pacific Journal of Mathematics, 243(2), 233-242. https://doi.org/10.2140/pjm.2009.243.233