Picard-Vessiot theory for real partial differential fields

TL;DR

This paper extends Picard-Vessiot theory to real partial differential fields, proving the existence of real Picard-Vessiot extensions, establishing a Galois correspondence, and characterizing real Liouville extensions.

Contribution

It introduces the theory of real Picard-Vessiot extensions for real partial differential fields, including existence, Galois correspondence, and characterization of Liouville extensions.

Findings

Existence of real Picard-Vessiot extensions proven.

Galois correspondence established for these extensions.

Characterization of real Liouville extensions provided.

Abstract

We prove the existence of real Picard-Vessiot extensions for real partial differential fields with real closed field of constants. We establish a Galois correspondence theorem for these Picard-Vessiot extensions and characterize real Liouville extensions of real partial differential fields.