Parallelisms & Lie Connections

TL;DR

This paper investigates rational parallelisms on algebraic varieties using Galois groups derived from Picard-Vessiot theory to understand the transcendence of their symmetries.

Contribution

It introduces a novel approach linking rational parallelisms with Galois groups from principal connections to analyze symmetry transcendence.

Findings

Established a connection between parallelisms and Galois groups

Provided criteria for symmetry transcendence in algebraic varieties

Enhanced understanding of symmetries via Picard-Vessiot theory

Abstract

The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of principal connections.