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