李代数上同调与结构  

Lie Algebra Cohomology and Structure

作　　者：李智龙[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《重庆与世界（学术版）》2014年第4期104-106,共3页THE WORLD & CHONG QING

摘　　要：研究李代数的第二上同调,给出第二上同调与同态集上方程的联系。通过李代数的上同调、ChevalleyEilenberg预解,以及Whitehead引理,给出一个"不存在维数小于3的半单李代数"的同调证明,并将同调理论和经典的结构理论作了一些联系。In this paper, the second cohomology of Lie algebra was studied and connected to equation o- ver homomorphism set. By Lie algebra cohomology, Chevalley-Eilenberg resolution and Whitehead lem- ma, a homological proof for ＂nonexistence of semisimple Lie algebra with dimension less than 3＂ is giv- en. Moreover, some connections between homology theory and classical structure theory are provided.

关 键 词：李代数 上同调 半单 方程 Chevalley—Eilenberg预解 Whitehead引理 

分 类 号：O154.2[理学—数学]