Title: On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebras
Abstract:We consider the lower central series 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 ce...We consider the lower central series 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 algebra Wn of polynomial vector fields on C n .We compute the space [An, An]/[An, [An, An]] and show that it is isomorphic to the space ΩRead More