[1]裴凤,周建华.Lie color 代数的商代数[J].东南大学学报(自然科学版),2004,34(6):865-868.[doi:10.3969/j.issn.1001-0505.2004.06.033]
 Pei Feng,Zhou Jianhua.Algebras of quotients of Lie color algebras[J].Journal of Southeast University (Natural Science Edition),2004,34(6):865-868.[doi:10.3969/j.issn.1001-0505.2004.06.033]
点击复制

Lie color 代数的商代数()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
34
期数:
2004年第6期
页码:
865-868
栏目:
数学、物理学、力学
出版日期:
2004-11-20

文章信息/Info

Title:
Algebras of quotients of Lie color algebras
作者:
裴凤 周建华
东南大学数学系, 南京 210096
Author(s):
Pei Feng Zhou Jianhua
Department of Mathematics, Southeast University, Nanjing 210096, China
关键词:
Lie color代数 商代数 半素性 本质理想 齐次偏导子
Keywords:
Lie color algebras algebras of quotients semiprimeness essential ideals homogeneous partial derivations
分类号:
O153.5
DOI:
10.3969/j.issn.1001-0505.2004.06.033
摘要:
介绍了Lie color 代数的一些性质,如素性、半素性、非退化性等.给出了Lie color 代数的商代数以及弱商代数的概念,并把Lie color 代数的素性和半素性推广到它的商代数上.利用没有非零零化子的理想对Lie color 代数的商代数进行刻画,证明了:若L是Lie color 代数Q的子代数,QL的商代数当且仅当Q理想吸收于L.通过具体构造证明了每一个半素Lie color 代数都有极大商代数,并给出这个极大商代数的等价刻画.
Abstract:
Some properties of Lie color algebra, such as semiprimeness, primeness and nondegeneracy are introduced. The notions of algebra of quotients and weak algebra of quotients of Lie color algebras are given. The semiprimeness and primeness are lifted from a Lie color algebra to its algebras of quotients. It is shown that if L is a subgroup of a Lie color algebra Q, then Q is an algebra of quotients of L if and only if Q is ideally absorbed into L. For every semiprime Lie color algebra, a maximal algebra of quotients is constructed.

参考文献/References:

[1] Utumi Y.On quotient rings [J]. Osaka J Math,1956,8:1-18.
[2] Molina N S.Algebras of quotients of Lie algebras [J]. J Pure and Applied Algebra, 2004,188:175-188.
[3] Scheunert M.Generalized Lie algebras [J].J Math Phys,1979,20(4):712-720.
[4] Passman D S.Simple Lie color algebras of Witt type [J]. J Algebra, 1998,208:698-721.

相似文献/References:

[1]裴凤,周建华.代数的交叉模[J].东南大学学报(自然科学版),2007,37(6):1137.[doi:10.3969/j.issn.1001-0505.2007.06.039]
 Pei Feng,Zhou Jianhua.Crossed modules for Lie color algebras[J].Journal of Southeast University (Natural Science Edition),2007,37(6):1137.[doi:10.3969/j.issn.1001-0505.2007.06.039]

备注/Memo

备注/Memo:
作者简介: 裴凤(1980—)女,硕士生; 周建华(联系人),男,博士,教授,jhzhou@seu.edu.cn.
更新日期/Last Update: 2004-11-20