TY - JOUR
T1 - On [A, A] / [A, [A, A]] and on a Wn-action on the consecutive commutators of free associative algebras
AU - Feigin, Boris
AU - Shoikhet, Boris
PY - 2007
Y1 - 2007
N2 - We consider the lower central series 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 Wn of polynomial vector fields on ℂn. We compute the space [An, An)/[A n, [An, An)) and show that it is isomorphic to the space Ωclosed2(ℂn) ⊕ Ωclosed4(ℂn) ⊕Ω closed6 (ℂn) ⊕ . . . .
AB - We consider the lower central series 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 Wn of polynomial vector fields on ℂn. We compute the space [An, An)/[A n, [An, An)) and show that it is isomorphic to the space Ωclosed2(ℂn) ⊕ Ωclosed4(ℂn) ⊕Ω closed6 (ℂn) ⊕ . . . .
UR - http://www.scopus.com/inward/record.url?scp=38849084583&partnerID=8YFLogxK
U2 - 10.4310/MRL.2007.v14.n5.a7
DO - 10.4310/MRL.2007.v14.n5.a7
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AN - SCOPUS:38849084583
SN - 1073-2780
VL - 14
SP - 781
EP - 795
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 5-6
ER -