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

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dc.creatorFeigin, Boris
dc.creatorShoikhet, Boris
dc.date2006-10-12
dc.date2006-10-16
dc.date.accessioned2026-07-07T07:29:01Z
dc.date.available2026-07-07T07:29:01Z
dc.descriptionWe 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 $Ω^2_{closed}(\mathbb{C}^n) \oplus Ω^4_{closed}(\mathbb{C}^n) \oplus Ω^6_{closed}(\mathbb{C}^n) \oplus ...$.
dc.description18 pages, 4 eps Figures, v2: minor corrections are made
dc.identifierhttps://arxiv.org/abs/math/0610410
dc.identifierhttp://arxiv.org/abs/math/0610410
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117945
dc.subjectQuantum Algebra
dc.subjectK-Theory and Homology
dc.titleOn $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebra
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