A general necessary and sufficient condition is obtained for a Kac module of the quantum general linear superalgebra to be simple. More explicit conditions are then obtained by considering separately the case where the quantum parameter is not a root of unity and the case where it is a root of unity.

中文翻译：

---

量子通用线性超代数的Kac模块的简单性

获得了量子一般线性超代数的Kac模简单的一般充要条件。然后，通过分别考虑量子参数不是统一根的情况和量子参数不是统一根的情况来获得更明确的条件。