A Carnot algebra is a graded nilpotent Lie algebra ⊕ · · · ⊕ generated by . The bi-dimension of the Carnot algebra is the pair (dim , dim ). 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.
Title: Rigid Carnot algebras: classification
Authors: A.A. Agrachev, A. Marigo
Journal title: Dynamical and Control Systems