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 PGL 3 -equivariant derivations on the coordinate rings of F-irreducible PGL 3 -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 PGL 3 .
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