Reference request: Carnot Algebra Let $G$ be a group and let $\Gamma_G(k)$ be the $k$th term of the lower central series of $G$. For each $k\geq 1$, set $\mathcal{L}_G(k)=\Gamma_G(k)/\Gamma_G(k+1)$ and $$\mathcal{L}_G:=\bigoplus_{k\geq 1}\mathcal{L}_G(k).$$ Then $\mathcal{L}_G$ has a graded Lie algebra structure induced from the commutator bracket on $G$.
I heard that $\mathcal{L}_G$ is called the Carnot Algebra. Could any one provide some reference of Carnot Algebras (definition, basic facts, etc.)? I never heard of this terminology; for all the papers that I have read, $\mathcal{L}_G$ is usually called the associated Lie algebra. 

This Algebra is called the Carnot group.
Google and search for "Carnot Groups and Carnot solvmanifolds".
