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 language | English |
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Pages (from-to) | 786-793 |
Number of pages | 8 |
Journal | Journal of Algebra |
Volume | 318 |
Issue number | 2 |
DOIs | |
State | Published - Dec 15 2007 |
Keywords
- Differential Galois theory
- Galois cohomology
- Generic extensions
- Picard-Vessiot