Relative D-groups and differential Galois theory in several derivations

TL;DR

This paper develops a Galois theory for logarithmic differential equations within the framework of relative D-groups in partial differential-algebraic geometry, extending the understanding of symmetries in differential equations.

Contribution

It introduces a novel Galois theory for logarithmic differential equations using relative D-groups in the context of partial differential-algebraic geometry.

Findings

Establishes a new Galois correspondence for logarithmic differential equations.

Extends differential Galois theory to the setting of relative D-groups.

Provides foundational results linking differential equations and algebraic groups in multiple derivations.

Abstract

The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.