2006/10/12 by Boris Feigin, Feigin, Boris, Boris Shoikhet +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0610410
18 pages, 4 eps Figures, v2: minor corrections are made
openalex publication_date 2006/10/12 · arxiv created 2006/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 algebra Wn of polynomial vector fields on ℂn. We compute the space [An,An]/[An,[An,An]] and show that it is isomorphic to the space Ω2closed(ℂn) ⊕ Ω4closed(ℂn) ⊕ Ω6closed(ℂn) ⊕ ....