Picard-Vessiot extensions with specified Galois group

Ted Chinburg; Lourdes Juan; Andy R. Magid

doi:10.2140/pjm.2009.243.233

Picard-Vessiot extensions with specified Galois group

Ted Chinburg, Lourdes Juan, Andy R. Magid

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	233-242
Number of pages	10
Journal	Pacific Journal of Mathematics
Volume	243
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2009.243.233
State	Published - Dec 2009

Keywords

Differential
Galois
Picard-Vessiot

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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.",

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Picard-Vessiot extensions with specified Galois group

Abstract

Keywords

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