TY - JOUR
T1 - On generic differential SOn-extensions
AU - Juan, Lourdes
AU - Ledet, Arne
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77950606350&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-07-09314-8
DO - 10.1090/S0002-9939-07-09314-8
M3 - Article
AN - SCOPUS:77950606350
SN - 0002-9939
VL - 136
SP - 1145
EP - 1153
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -