Solvable-by-finite groups as differential Galois groups

Mitschi, Claude; Singer, Michael F.

HAL, hal-00129674 / Harvested from HAL

Résumé

We prove the inverse problem of differential Galois theory over the differential field k=C(x), where C is an algebraic closed field of characteristic zero, for linear algebraic groups G over CC with a solvable identity component G°. We show that for any k-irreducible principal homogeneous space V for G, the derivation d/dx of k can be extended on k(V) in such a way that k(V) is a Picard-Vessiot extension of k with Galois group G. The proof is constructive up to the finite embedding problem of classicalGalois theory over C(x).

Publié le : 2002-08-08
Classification: Algebraic group, Lie algebra, "Algebraic group, principal homogeneous space, differential Galois group, inverse problem, Lie algebra.", 12H05, 20G99,12F12, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]

@article{hal-00129674,
     author = {Mitschi, Claude and Singer, Michael F.},
     title = {Solvable-by-finite groups as differential Galois groups},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129674}
}

Mitschi, Claude; Singer, Michael F. Solvable-by-finite groups as differential Galois groups. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129674/