A Jordan-Hoelder Theorem for Differential Algebraic Groups

TL;DR

This paper establishes a Jordan-Hölder type theorem for differential algebraic groups, demonstrating their structure through a finite series of almost simple groups and classifying these in the ordinary differential case.

Contribution

It introduces a finite subnormal series for differential algebraic groups with almost simple quotients and classifies these groups in the ordinary differential case.

Findings

Existence of a finite subnormal series with almost simple quotients

Uniqueness of the series under certain conditions

Classification of almost simple linear differential algebraic groups in the ordinary case

Abstract

We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is have no normal subgroups of the same type. We give a uniqueness result, prove several properties of almost simple groups and, in the ordinary differential case, classify almost simple linear differential algebraic groups.