On universal Lie nilpotent associative algebras

被引：19

作者：

Etingof, Pavel ^{[1
]}

Kim, John

Ma, Xiaoguang ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

JOURNAL OF ALGEBRA | 2009年 / 321卷 / 02期

关键词：

Lie nilpotent algebra; Lower central series;

D O I：

10.1016/j.jalgebra.2008.09.042

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We Study the quotient Q(i)(A) of a free algebra A by the ideal M-i(A) generated by the ith 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 M-i(A), e.g. when M-i(A)M-j(A) is contained in Mi+j-1 (A) (by a result Of Gupta and Levin, it is always contained ill Mi+j-2(A)). (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：697 / 703

页数：7