Real difference Galois theory

TL;DR

This paper develops a difference Galois theory tailored for real fields, establishing foundational concepts like the real Picard-Vessiot extension and the real difference Galois group, along with a Galois correspondence.

Contribution

It introduces the first comprehensive difference Galois theory framework specifically for real fields, including existence, uniqueness, and Galois correspondence results.

Findings

Existence and uniqueness of real Picard-Vessiot extensions

Definition of the real difference Galois group

Galois correspondence established for real difference fields

Abstract

In this paper, we develop a difference Galois theory in the setting of real fields. After proving the existence and uniqueness of the real Picard-Vessiot extension, we define the real difference Galois group and prove a Galois correspondence.