Loading...
Please wait, while we are loading the content...
Similar Documents
Picard-Vessiot extensions of real differential fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Crespo, Teresa Fernández Hajto, Zbigniew |
| Copyright Year | 2014 |
| Abstract | For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a unique formally real Picard- Vessiot extension up to K-differential automorphism. However such an equation may have Picard-Vessiot extensions which are not formally real fields. The differential Galois group of a Picard-Vessiot extension for this equation has the structure of a linear algebraic group defined over k and is a k-form of the differential Galois group H of the equation over the differential field K(i), where i denotes a square root of -1 in the algebraic closure of k. These facts lead us to consider two issues: determining the number of K-differential isomorphism classes of Picard-Vessiot extensions and describing the variation of the differential Galois group in the set of k-forms of H. We address these two issues in the cases when H is a special linear, a special orthogonal, or a symplectic linear algebraic group and conclude that there is no general behaviour. |
| File Format | PDF HTM / HTML |
| DOI | 10.3842/SIGMA.2019.100 |
| Alternate Webpage(s) | https://fr.arxiv.org/pdf/1403.3226.pdf |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1403.3226 |
| Alternate Webpage(s) | https://mat.ub.edu/EMIS/journals/SIGMA/2019/100/sigma19-100.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1403.3226v3.pdf |
| Alternate Webpage(s) | https://doi.org/10.3842/SIGMA.2019.100 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
