Title: Rigid Carnot algebras: classification
Authors: A.A. Agrachev, A. Marigo
Journal title: Dynamical and Control Systems
Year: 2005
Volume: 11
Pages: 449-494
Abstract:

A Carnot algebra is a graded nilpotent Lie algebra $$L = L1$$ ⊕ · · · ⊕ $$L_r$$ generated by $$L_1$$. The bi-dimension of the Carnot algebra $$L$$ is the pair (dim $$L_1$$, dim $$L$$). A Carnot algebra is called rigid if it is isomorphic to any of its small perturbations in the space of Carnot algebras of the prescribed bi-dimension. In this paper we give a complete classification of rigid Carnot algebras. Besides free nilpotent Lie algebras there are two infinite series and 29 exceptional rigid algebras of 16 exceptional bi-dimensions.