## Abstract

We show how to produce SO_{n}-equivariant vector fields on non-trivial SO_{n}-torsors which correspond to quadratic forms non-equivalent to the unit form. For n ≥ 3 we then give an example of a Picard-Vessiot extension with group SO_{n} which is the function field of a non-trivial SO_{n}-torsor.

Original language | English |
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Pages (from-to) | 735-745 |

Number of pages | 11 |

Journal | Journal of Algebra |

Volume | 316 |

Issue number | 2 |

DOIs | |

State | Published - Oct 15 2007 |

## Keywords

- Differential Galois theory
- Galois cohomology
- Picard-Vessiot extensions
- Quadratic forms
- Special orthogonal groups
- Torsors

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