TY - JOUR

T1 - Pure Picard-Vessiot extensions with generic properties

AU - Juan, Lourdes

PY - 2004/9

Y1 - 2004/9

N2 - Given a connected linear algebraic group G over an algebraically closed field C of characteristic 0, we construct a pure Picard-Vessiot extension for G, namely, a Picard-Vessiot extension ε ⊃ ℱ, with differential Galois group G, such that ε and ℱ are purely differentially transcendental over C. The differential field ε is the quotient field of a G-stable proper differential subring ℛ with the property that if F is any differential field with field of constants C and E ⊃ F is a Picard-Vessiot extension with differential Galois group a connected subgroup H of G, then there is a differential homomorphism ø: ℛ → E such that E is generated over F as a differential field by ø(ℛ).

AB - Given a connected linear algebraic group G over an algebraically closed field C of characteristic 0, we construct a pure Picard-Vessiot extension for G, namely, a Picard-Vessiot extension ε ⊃ ℱ, with differential Galois group G, such that ε and ℱ are purely differentially transcendental over C. The differential field ε is the quotient field of a G-stable proper differential subring ℛ with the property that if F is any differential field with field of constants C and E ⊃ F is a Picard-Vessiot extension with differential Galois group a connected subgroup H of G, then there is a differential homomorphism ø: ℛ → E such that E is generated over F as a differential field by ø(ℛ).

UR - http://www.scopus.com/inward/record.url?scp=4344643825&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-04-07390-3

DO - 10.1090/S0002-9939-04-07390-3

M3 - Article

AN - SCOPUS:4344643825

SN - 0002-9939

VL - 132

SP - 2549

EP - 2556

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -