摘要
在前人研究的基础上,本研究提出了李代数经过两次莱布尼兹代数的阿贝尔扩张仍为李代数的问题。首先,根据莱布尼兹代数的阿贝尔扩张的定义,得到李代数通过的阿贝尔扩张仍然为李代数。随后,对李代数进行阿贝尔扩张,定义了上的括号,并证明其为李代数。
In this paper,the problem that the Lie algebra which is still a Lie algebra through twice abelian extension of Leibniz algebra is proposed based on the previous studies. Firstly,according to the definition of the abelian extension of Leibniz algebra,we can obtain that the abelian extension of Lie algebra by is still a Lie algebra. And then we obtain the extension of Lie algebra and define a bracket on the extension. Moreover we can prove that the abelian extension of Leibniz algebra is still a Lie algebra.
出处
《南昌航空大学学报（自然科学版）》
CAS
2016年第1期28-31,共4页
Journal of Nanchang Hangkong University(Natural Sciences)
基金
国家自然科学基金(11126338
11461047
11201218)
关键词
李代数
莱布尼兹代数的表示
莱布尼兹代数的阿贝尔扩张
正合序列
Lie algebra
the representation of the Leibniz algebra
the abelian extension of Leibniz algebra
exact sequence
