Homogeneous models of C3 Monge geometries

TL;DR

This paper classifies homogeneous models of C3 Monge geometries in eight dimensions, linking Monge distributions to simple Lie algebras and parabolic geometries, advancing understanding of their structure and classification.

Contribution

It provides a classification of homogeneous C3 Monge geometries in dimension eight, using a new algorithm and extending prior work on these distributions.

Findings

Classification of homogeneous C3 Monge geometries achieved

Connection established between Monge distributions and simple Lie algebras

Development of a general classification algorithm

Abstract

Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to the classification problem for homogeneous models of Monge distributions of type C3 in dimension eight, and is complementary to a paper by I. Anderson and P. Nurowski. The general classification algorithm, as well as most of its application to the particular problem, are joint work with Ian Anderson.