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Rigid Carnot algebras: Classification Andrei Agrachev
 

Summary: Rigid Carnot algebras: Classification
Andrei Agrachev
SISSA, Trieste,
Italy
agrachev@sissa.it
Alessia Marigo
Universit`a di Roma "La Sapienza",
Italy
marigo@mat.uniroma1.it
Abstract
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.
1 Introduction
One main motivation to study Carnot algebras is their role as local nilpotent
approximations of regular vector distributions.

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics