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

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We show how to produce SOn-equivariant vector fields on non-trivial SOn-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 SOn which is the function field of a non-trivial SOn-torsor.

Original languageEnglish
Pages (from-to)735-745
Number of pages11
JournalJournal of Algebra
Issue number2
StatePublished - Oct 15 2007


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


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