On a generic inverse differential Galois problem for GL_n
| dc.creator | Juan, Lourdes | |
| dc.date | 2000-12-08 | |
| dc.date | 2001-04-12 | |
| dc.date.accessioned | 2026-07-07T04:39:07Z | |
| dc.date.available | 2026-07-07T04:39:07Z | |
| dc.description | \newcommand{\GLn}{\operatorname{GL}_n} \newcommand{\GL}{\GLn(C)} Let $F$ be a differential field with algebraically closed field of constants $C$. We prove that $F< Y_{ij}>(X_{ij})\supset F< Y_{ij}>$ is a generic Picard-Vessiot extension of $F$ for $\GL$. If $E\supset F$ is any Picard-Vessiot extension with differential Galois group $\GL$ then $E\cong F(X_{ij})$ as $F$- and $\GL$-modules and there are $f_{ij}\in F$ such that $F< Y_{ij}>(X_{ij})\supset F< Y_{ij}>$ specializes to $E\supset F$ via $ Y_{ij}\mapsto f_{ij}$. The $[f_{ij}]\in M_n(F)$ for which the image of the map $ Y_{ij}\mapsto f_{ij}$ is a Picard-Vessiot extension of $F$ with group $\GL$ can be characterized as those $[f_{ij}]\in M_n(F)$ for which the wronskians of the monomials in $F< Y_{ij}>(X_{ij})$ of degree less than or equal to $k$ all map to non-zero elements under $ Y_{ij}\mapstof_{ij}$. | |
| dc.identifier | https://arxiv.org/abs/math/0012063 | |
| dc.identifier | http://arxiv.org/abs/math/0012063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60535 | |
| dc.subject | Rings and Algebras | |
| dc.title | On a generic inverse differential Galois problem for GL_n | |
| dc.type | text |