On universal Lie nilpotent associative algebras

JOURNAL OF ALGEBRA

卷:321

Article

Etingof, Pavel¹  Ma, Xiaoguang¹ 

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

关键词: Lie nilpotent algebra;    Lower central series;   

DOI  :  10.1016/j.jalgebra.2008.09.042

来源: Elsevier

【 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.

【 授权许可】

Free