On the three-dimensional cohomology group of Lie algebras.
On the three-dimensional cohomology group of Lie algebras.
复制标题
关于李代数的三维上同调群。
DOI：
10.2969/jmsj/00520171
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发表时间：
1953
影响因子：
0.7
通讯作者：
M. Mori
中科院分区：
文献类型：
--
作者：
M. Mori
Eilenberg和MacLane [1]利用上同调理论建立了一个类似于在给定域上具有固定分裂域的正规单代数的Brauer群理论的群论：以固定交换群G为中心的Q-核的相似类理论。他们得到了Q-核的相似类群同构于交换系数群G上Q的三维上同调群H^{3}（Q，G）的一个显著结果，并利用二维上同调理论回答了Baer [21]关于群扩张的问题.另一方面，Chevalley和Eilenberg [3]证明了L $关于交换李代数Z$的二维上同调群H^{2}（L，Z，P）$和L$在上的表示P$
Eilenberg and MacLane [1] have built up, by means of the cohomology theory, an analogue in the theory of groups to the theory of the Brauer group of normal simple algebras with a fixed splitting field over a given field: The theory of similarity classes of Q-kernels with a fixed abelian group $G$ as center. They arrived at a remarkable result that the group of similarity classes of Q-kernels is isomorphic to the three-dimensional cohomology group $H^{3}(Q, G)$ of $Q$ over the abelian coefficient group $G$ , and gave an answer to the problem of Baer [21 on group extensions in terms of the two-dimensional cohomology theory. On the other hand, Chevalley and Eilenberg [3] have shown that the two-dimensional cohomology group $H^{2}(L, Z, P)$ of a Lie algebra $L$ with respect to an abelian Lie algebra $Z$ and a representation $P$ of $L$ over