Picard-Vessiot extensions with specified Galois group

Ted Chinburg, Lourdes Juan, Andy R. Magid

Research output: Contribution to journalArticle

Abstract

Picard-Vessiot extensions are determined by their differential module structure. For a fixed group G, Picard-Vessiot extensions with differential Galois group G are all isomorphic as G-modules but not as differential rings. We show that isomorphism classes of Picard-Vessiot extensions with group G correspond to G-orbits in a certain finite-dimensional vector space with G-action.

Original languageEnglish
Pages (from-to)233-242
Number of pages10
JournalPacific Journal of Mathematics
Volume243
Issue number2
DOIs
StatePublished - Dec 2009

Keywords

  • Differential
  • Galois
  • Picard-Vessiot

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