有关超群表示的一些性质

Some Properties of the Super Representations

定义超群G在超空间V上的一个超线性表示,并将其线性扩充到群代数C[G]上,从而构造出一个C[G]-超模结构;并给出超空间V上的内积〈,〉运算,讨论该内积关于G作用下不变时所具有的性质;同时推广了马施克定理及舒尔引理。

A super l inear representation of the super group G on a super space V is defined, and extended it to the group algebra C[G] to obtain a super module structure on V. An inner product operation〈,〉on the super space V is defined, and its property of invariance under the action of G is discussed. In the mean-time, the Maschkes’ theorem and Schur’s lemma have been generalized to the super case.