用GAP计算生成长度
Computations of generating lengths with GAP
摘要：
本文讨论了在模表示理论中如何应用GAP进行计算。特别感兴趣的是生成数的群代数，它衡量的失败的生成假设的稳定模范畴。我们介绍了一种计算方法来做这个计算，并在伪代码。我们还在GAP中实现了该算法，并成功地完成了以前无法完成的示例计算。这些计算导致对群$Q_8$和$A_4$的鬼数的计算。
英文摘要：
In this paper, we discuss how to apply GAP to do computations in modular representation theory. Of particular interest is the generating number of a group algebra, which measures the failure of the generating hypothesis in the stable module category. We introduce a computational method to do this calculation and present it in pseudo-code. We have also implemented the algorithm in GAP and managed to do computations of examples that we were not able to do before. The computations lead to conjectures on the ghost numbers of the groups $Q_8$ and $A_4$.
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