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Статья

On [A,A]/[A, [A,A]] and on a Wn-action on the consecutive commutators of free associative algebra

Mathematical Research Letters. 2007. Vol. 14. No. 5. P. 781-795.
Feigin B. L., Shoikhet B.
We consider the lower central filtration of the free associative algebra An 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 algebraWn of polynomial vector fields on Cn. We compute the space [An,An]/[An, [An,An]] and show that it is isomorphic to the space 2 closed(Cn) ⊕ 4 closed(Cn) ⊕ 6closed(Cn)