Rigid Carnot algebras: classification

A Carnot algebra is a graded nilpotent Lie algebra L = L1 ⊕ ⋯ ⊕Lr generated by L1. The bidimension of the Carnot algebra L is the pair (dim L1, dim L). A Carnot algebra is said to be rigid if it is isomorphic to any of its small perturbations in the space of Carnot algebras of the prescribed bidimension. In this paper, we give a complete classification of rigid Carnot algebras. In addition to free nilpotent Lie algebras, there are two infinite series and 29 exceptional rigid algebras of 16 exceptional bidimensions.