Picard-Vessiot extensions for real fields
نویسندگان
چکیده
منابع مشابه
Quasialgebraicity of Picard–vessiot Fields
We prove that under certain spectral assumptions on the monodromy group, solutions of the Fuchsian system of linear equations on the Riemann sphere admit explicit global bounds on the number of their isolated zeros.
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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...
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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.
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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 Picard-vessiot Extensions for Connected-by-finite Groups
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.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2010-10700-1