TY - JOUR

T1 - On generic differential SOn-extensions

AU - Juan, Lourdes

AU - Ledet, Arne

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

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

VL - 136

SP - 1145

EP - 1153

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -