Equivariant vector fields on non-trivial SOn-torsors and differential Galois theory

Lourdes Juan; Arne Ledet

doi:10.1016/j.jalgebra.2007.01.005

Equivariant vector fields on non-trivial SO_n-torsors and differential Galois theory

Lourdes Juan, Arne Ledet

Mathematics and Statistics

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6 Scopus citations

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
Pages (from-to)	735-745
Number of pages	11
Journal	Journal of Algebra
Volume	316
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2007.01.005
State	Published - Oct 15 2007

Keywords

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

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10.1016/j.jalgebra.2007.01.005

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KW - Galois cohomology

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KW - Quadratic forms

KW - Special orthogonal groups

KW - Torsors

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Equivariant vector fields on non-trivial SO_n-torsors and differential Galois theory

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Keywords

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