## Abstract

Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C(Y_{ij}),with Y_{ij},1 ≤ i ≤ n - 1, 1 ≤ j ≤ n, i ≤ j, differentially independent indeterminates over C. We show that there is a Picard-Vessiot extension ε F for a matrix equation X' = XA(Y_{ij}), with differential Galois group SO_{n}, with the property that if F is any differential field with field of constants C, then there is a Picard- Vessiot extension E F with differential Galois group H ≤ SO_{n} if and only if there are f_{ij} ε F with A(f_{ij}) well defined and the equation X' = XA(f _{ij}) giving rise to the extension E F.

Original language | English |
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Pages (from-to) | 1145-1153 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 136 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2008 |

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