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.

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