Schur引理的推广与应用

Graded Schur's Lemma and its Application

首先,在模(表示)理论中的一个Schur引理的基础上,推广得到“阶化”Schur引理,一般的Schur引理是“阶化”Schur引理的特殊情形。然后,作为Schur引理的一个应用,在李代数模的Casimir元素的基础上,定义并讨论了李超代数模的Casimir元素,得出了李超代数模的Casimir元素是数乘变换的一个充分条件。

First, based on the Schur＇s Lemma in the representation theory, we generalize it into the graded Schur＇s Lemma, and the usual Schur＇s Lemma is a special case of the graded Schur＇s Lemma. Then, as an application of the Schufs Lemma, based on the Casimir element of modules of Lie algebras, we define and discuss the Casimir element of modules of Lie superalgebras, and prove when it is the scalar multiplication.