Generic Picard-vessiot Extensions for Connected-by-finite Groups
نویسندگان
چکیده
We construct generic Picard-Vessiot extensions for linear algebraic groups which are isomorphic to the semidirect product of a connected group G by an arbitrary finite group H, where the adjoint H-action on the Lie algebra of G is faithful.
منابع مشابه
Generic Picard-vessiot Extensions for Non-connected Groups
Abstract. Let K be a differential field with algebraically closed field of constants C and G a linear algebraic group over C. We provide a characterization of the K-irreducible G-torsors for nonconnected groups G in terms of the first Galois cohomology H(K, G) and use it to construct Picard-Vessiot extensions which correspond to non-trivial torsors for the infinite quaternion group, the infinit...
متن کاملGeneric Rings for Picard–Vessiot Extensions and Generic Differential Equations
Let G be an observable subgroup of GLn. We produce an extension of differential commutative rings generic for Picard–Vessiot extensions with
متن کاملGeneric Picard-vessiot Extensions and Generic Equations
The notion of a generic Picard-Vessiot extension with group G is equivalent to that of a generic linear differential equation for the same group.
متن کاملA pr 2 00 1 ON A GENERIC INVERSE DIFFERENTIAL GALOIS PROBLEM FOR GL
In this paper we construct a generic Picard-Vessiot extension for the general linear groups. In the case when the differential base field has finite transcen-dence degree over its field of constants we provide necessary and sufficient conditions for solving the inverse differential Galois problem for this groups via specialization from our generic extension.
متن کاملOn Picard–Vessiot extensions with group PGL3
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 n...
متن کامل