On universal Lie nilpotent associative algebras
Author(s)Etingof, Pavel I.; Kim, John; Ma, Xiaoguang
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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)).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Algebra
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.
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