论文标题
$ \ frak {sl}（2）$及其在主要特征中的应用
Cohomology of $\frak{sl}(2)$ and its applications in prime characteristic
论文作者
论文摘要
在一个特征性$ p> 2的领域，$在所有简单模块中都确定了三维简单谎言代数$ \ frak {sl}（2）$的第一个共同体，在所有简单模块中都确定了系数，这意味着Whitehead的第一个Lemma在主要特征中并非如此。作为应用程序，在任何简单模块上的$ \ frak {sl}（2）$的应用程序和2个本地推导也被表征。
Over a field of characteristic $p>2,$ the first cohomology of the 3-dimensional simple Lie algebra $\frak{sl}(2)$ with coefficients in all simple modules is determined, which implies Whitehead's first lemma is not true in prime characteristic. As applications, derivations and 2-local derivations of $\frak{sl}(2)$ on any simple module are also be characterized.
