On universal Lie nilpotent associative algebras
Name
Etingof-2009-On universal Lie nil.pdf
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Author(s)
Etingof, Pavel I.
Kim, John
Ma, Xiaoguang
Date Issued
January 2009
Journal
Journal of Algebra
Publisher
Elsevier B.V.
Citation
Etingof, Pavel, John Kim, and Xiaoguang Ma. “On Universal Lie Nilpotent Associative Algebras.” Journal of Algebra 321, no. 2 (January 2009): 697–703. © 2008 Elsevier Inc.
Version
Final published version
Abstract
We study the quotient Qi(A) of a free algebra A by the ideal Mi (A) generated by the i th commutator of any elements. In particular, we completely describe such quotient for i=4 (for i 3 this was done previously by Feigin and Shoikhet). We also study properties of the ideals Mi(A), e.g. when Mi(A)Mj(A) is contained in M[subscript i+j-1](A) (by result of Gupta and Levin, it is always contained in M[subscript i+j-2](A)).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1016/j.jalgebra.2008.09.042
