On Picard-Vessiot extensions with group PGL3

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Abstract

Let F be a differential field of characteristic zero with algebraically closed field of constants. We provide an explicit description of the twisted Lie algebras of PGL3-equivariant derivations on the coordinate rings of F-irreducible PGL3-torsors in terms of nine-dimensional central simple algebras over F. We use this to construct a Picard-Vessiot extension which is the function field of a non-trivial torsor and which is a generic extension for PGL3.

Original languageEnglish
Pages (from-to)786-793
Number of pages8
JournalJournal of Algebra
Volume318
Issue number2
DOIs
StatePublished - Dec 15 2007

Keywords

  • Differential Galois theory
  • Galois cohomology
  • Generic extensions
  • Picard-Vessiot

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