On Picard-Vessiot extensions with group PGL3

[摘要] 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). (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] differential Galois theory;Galois cohomology;generic extensions;Picard-Vessiot