Linear Algebraic Groups as Parameterized Picard-Vessiot Galois Groups

Abstract

We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x' = 1, for certain differential fields k, if and only if its identity component has no one dimensional quotient as a linear algebraic group.

18 pages

References in corpus (1)

• Existence of $\partial$-parameterized Picard-Vessiot extensions over fields with algebraically closed constants