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.
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页码：697 / 703
页数：7
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