On universal Lie nilpotent associative algebras
Abstract
We study the quotient Qi(A) of a free algebra A by the ideal Mi(A) generated by relation that the i-th commutator of any elements is zero. 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 Mi+j-1(A) (by a result of Gupta and Levin, it is always contained in Mi+j-2(A)).
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