Picard–Vessiot extensions with specified Galois group

Ted Chinburg, Lourdes Juan and Andy R. Magid

Vol. 243 (2009), No. 2, 233–242

DOI: 10.2140/pjm.2009.243.233

Abstract

Picard–Vessiot extensions are determined by their differential module structure. For a fixed group G, Picard–Vessiot extensions with differential Galois group G are all isomorphic as G-modules but not as differential rings. We show that isomorphism classes of Picard–Vessiot extensions with group G correspond to G-orbits in a certain finite-dimensional vector space with G-action.

Keywords

differential, Galois, Picard–Vessiot

Mathematical Subject Classification 2000

Primary: 12H05, 34M15

Secondary: 12H20

Milestones

Received: 19 January 2009

Revised: 13 April 2009

Accepted: 14 April 2009

Published: 1 December 2009