Generic Picard–Vessiot Extensions for Nonconnected Groups

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Let K be a differential field with algebraically closed field of constants 𝒞 and G a linear algebraic group over 𝒞. We provide a characterization of the K-irreducible G-torsors for nonconnected groups G in terms of the first Galois cohomology H1(K, G) and use it to construct Picard–Vessiot extensions which correspond to nontrivial torsors for the infinite quaternion group, the infinite multiplicative and additive dihedral groups and the orthogonal groups. The extensions so constructed are generic for those groups.

Original languageEnglish
Pages (from-to)2989-3004
Number of pages16
JournalCommunications in Algebra
Issue number7
StatePublished - Jul 2 2016


  • Differential
  • Galois
  • Generic
  • Torsors


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