On Carnot algebra with the growth vector (2,3,5,8)

TL;DR

This paper constructs explicit vector field models for a specific Carnot algebra with growth vector (2,3,5,8) and identifies an infinitesimal symmetry of its sub-Riemannian structure.

Contribution

It provides explicit models and symmetry analysis for the Carnot algebra with growth vector (2,3,5,8), advancing understanding of its geometric structure.

Findings

Explicit vector field models of the Carnot algebra (2,3,5,8)

Identification of an infinitesimal symmetry in the sub-Riemannian structure

Enhanced understanding of the algebra's geometric properties

Abstract

We compute two vector field models of the Carnot algebra with the growth vector (2,3,5,8), and an infinitesimal symmetry of the corresponding sub-Riemannian structure.