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

Boris Feigin*, Boris Shoikhet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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) ⊕ . . . .

Original languageEnglish
Pages (from-to)781-795
Number of pages15
JournalMathematical Research Letters
Volume14
Issue number5-6
DOIs
StatePublished - 2007
Externally publishedYes

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