A Generic Picard-vessiot Extension with Group So3
نویسندگان
چکیده
Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C〈Y1, . . . , Y5〉, with Y1, . . . , Y5 differentially independent over C. We show that there is a Picard-Vessiot extension E ⊃ F for a matrix equation X ′ = XA(Yi), with differential Galois group SO3, with the property that if F is any differential field with field of constants C then there is a Picard-Vessiot extension E ⊃ F with differential Galois group H ≤ SO3 if and only if there are fi ∈ F with A(fi) well defined and the equation X ′ = XA(fi) giving rise to the extension E ⊃ F .
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