Summary: Rigid Carnot algebras: Classification
Universit`a di Roma "La Sapienza",
A Carnot algebra is a graded nilpotent Lie algebra L = L1 · · · Lr
generated by L1. The bi-dimension of the Carnot algebra L is the pair
(dim L1, 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.
One main motivation to study Carnot algebras is their role as local nilpotent
approximations of regular vector distributions.