A Cornucopia of Carnot Groups in Low Dimensions

Abstract Stratified groups are those simply connected Lie whose algebras admit a derivation for which the eigenspace with eigenvalue 1 is generating. When stratified group equipped left-invariant path distance that homogeneous respect to automorphisms induced by derivation, this metric space known as Carnot group. appear in several mathematical contexts. To understand their algebraic structure, it useful study some examples explicitly. In work, we provide list of low-dimensional groups, express product, and present basis vector fields, together respective 1-forms, right-invariant other properties. We exhibit all dimension up 7 also free-nilpotent 14.