  We consider the lower central filtration of the free associative algebra
$A_n$ with $n$ generators as a Lie algebra. We consider the associated graded
Lie algebra. It is shown that this Lie algebra has a huge center which belongs
to the cyclic words, and on the quotient Lie algebra by the center there acts
the Lie algebra $W_n$ of polynomial vector fields on $\mathbb{C}^n$. We compute
the space $[A_n,A_n]/[A_n,[A_n,A_n]]$ and show that it is isomorphic to the
space $\Omega^2_{closed}(\mathbb{C}^n) \oplus \Omega^4_{closed}(\mathbb{C}^n)
\oplus \Omega^6_{closed}(\mathbb{C}^n) \oplus ...$.
