On universal Lie nilpotent associative algebras

Author(s)
Etingof, Pavel I.; Kim, John; Ma, Xiaoguang
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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)).
Date issued
2009-01
URI
http://hdl.handle.net/1721.1/96327
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
00218693
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