A Carnot algebra is a graded nilpotent Lie algebra L = L{sub}1 {direct +} · · · {direct +}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, while it is said to be semi-rigid if it admits only a finite number of deformations: any small perturbation gives a finite number of nonisomorphic rigid Carnot algebras. A complete classification of rigid Carnot algebras was given in a previous work [2]. In this paper, we concentrate on the classification of semi-rigid cases and their normal form.
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机译：卡诺代数是由L {sub} 1生成的梯度幂等李代数L = L {sub} 1 {direct +}···{direct +} L {sub} r。卡诺代数L的双偶对是（对角L {sub} 1，对角L）。如果卡诺代数与规定的双角卡诺代数空间中的任何小扰动同构，则称其为刚性;而如果仅允许有限数量的变形，则称其为半刚性。摄动给出了有限数量的非同构刚性卡诺代数。以前的工作[2]给出了刚性卡诺代数的完整分类。在本文中，我们集中于半刚性案例的分类及其正常形式。
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