Rigid Carnot Algebras: A Classification

A Carnot algebra is a graded nilpotent Lie algebra L = L sub(1) [oplus] [mldr ] [oplus] L sub(r) generated by L sub(1). The bidimension of the Carnot algebra L is the pair (dim L sub(1), dim L). A Carnot algebra is said to be rigid if it is isomorphic to any of its small perturbations in the space o...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2005-10, Vol.11 (4), p.449-494
Main Authors: Agrachev, A., Marigo, A.
Format: Article
Language:English
Subjects:
Algebra
Classification
Control systems
Infinite series
Lie groups
Perturbation
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Summary:A Carnot algebra is a graded nilpotent Lie algebra L = L sub(1) [oplus] [mldr ] [oplus] L sub(r) generated by L sub(1). The bidimension of the Carnot algebra L is the pair (dim L sub(1), 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.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-005-8816-9