On universal Lie nilpotent associative algebras

2008/05/13 by Pavel Etingof, John Kim, Etingof, Pavel +3 · 1 citation
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.0805.1909

7 pages

arxiv created 2008/05/13 · arxiv updated 2009/12/01

Abstract

We study the quotient Q_i(A) of a free algebra A by the ideal M_i(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 M_i(A), e.g. when M_i(A)M_j(A) is contained in M_i+j-1(A) (by a result of Gupta and Levin, it is always contained in M_i+j-2(A)).

Cited by

• Lower central series of free algebras in symmetric tensor categories

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