An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups

TL;DR

This paper introduces a new method for constructing the Rumin complex on homogeneous nilpotent Lie groups, utilizing ideas from parabolic geometry, and provides explicit computations for the Engel group.

Contribution

It offers an alternative construction of the Rumin complex on homogeneous nilpotent Lie groups, distinct from the classical approach on Carnot groups, with explicit examples.

Findings

New construction method for Rumin complex

Explicit computations for Engel group

Bridges parabolic geometry with Lie group analysis

Abstract

In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to the classical one on Carnot groups using ideas from parabolic geometry. We also give the explicit computations for the Engel group with this approach.