On generic differential SOn-extensions

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Abstract

Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C(Yij),with Yij,1 ≤ i ≤ n - 1, 1 ≤ j ≤ n, i ≤ j, differentially independent indeterminates over C. We show that there is a Picard-Vessiot extension ε F for a matrix equation X' = XA(Yij), with differential Galois group SOn, 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 ≤ SOn if and only if there are fij ε F with A(fij) well defined and the equation X' = XA(f ij) giving rise to the extension E F.

Original languageEnglish
Pages (from-to)1145-1153
Number of pages9
JournalProceedings of the American Mathematical Society
Volume136
Issue number4
DOIs
StatePublished - Apr 2008

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