English

On universal Lie nilpotent associative algebras

Rings and Algebras 2008-05-14 v1 Representation Theory

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)).

Keywords

Cite

@article{arxiv.0805.1909,
  title  = {On universal Lie nilpotent associative algebras},
  author = {Pavel Etingof and John Kim and Xiaoguang Ma},
  journal= {arXiv preprint arXiv:0805.1909},
  year   = {2008}
}

Comments

7 pages

R2 v1 2026-06-21T10:40:03.354Z