Leibniz代数的通用包络代数

J4 ›› 2013, Vol. 51 ›› Issue (02): 195-198.

Leibniz代数的通用包络代数

关宝玲^1,2, 陈良云²

1. 齐齐哈尔大学理学院, 黑龙江齐齐哈尔 161006|2. 东北师范大学数学与统计学院, 长春 130024

收稿日期:2012-06-18 出版日期:2013-03-26 发布日期:2013-03-27
通讯作者: 陈良云 E-mail:chenly640@nenu.edu.cn

Universal Enveloping Algebras of Leibniz Algebras

GUAN Baoling^1,2, CHEN Liangyun^2

1. College of Sciences, Qiqihar University, Qiqihar 161006, Heilongjiang Province, China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received:2012-06-18 Online:2013-03-26 Published:2013-03-27
Contact: CHEN Liangyun E-mail:chenly640@nenu.edu.cn

摘要/Abstract

摘要：

把李代数通用包络代数的性质推广到Leibniz代数, 给出了Leibniz代数L的通用包络代数U(L)的定义, 并利用该定义得到了U(L)的生成元集, 确定了U(L)的唯一性定理和U(L)模结构定理, 证明了通用包络代数U(L)的存在性.

关键词: Leibniz代数, 通用包络代数, 生成元集

Abstract:

The authors generalized some properties of the universal enveloping algebras for Lie algebras to Leibniz algebras, and gave the definition of universal enveloping algebras U(L) of Leibniz algebras L, by means of the definition of universal enveloping algebras, obtained a set of generators f
or U(L), and determined U(L)’s uniqueness theorem and U(L)module’s structure theorem. Moreover, the existence of universal enveloping algebras U(L) was proved.

Key words: Leibniz algebras, universal enveloping algebras, set of generators

中图分类号:

O152.5

关宝玲, 陈良云. Leibniz代数的通用包络代数[J]. J4, 2013, 51(02): 195-198.

GUAN Bao-Ling, CHEN Liang-Yun. Universal Enveloping Algebras of Leibniz Algebras[J]. J4, 2013, 51(02): 195-198.

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