On a derived equivalence classification for blocks of finite groups

Broue的阿贝尔缺陷群猜想是有限群模表示理论中的一个重要问题。该猜想表明，具有阿贝尔缺陷群的有限群的块将被导出为等价于它的布劳尔对应块。在这个项目中，我为这个猜想计算了一些例子，并试图推广这些结果。对于平凡的源模块，我也得到了一些结果，这对于构造稳定等价，计算简单模块在稳定等价下的像的模是很重要的。

Broue's abelian defect group conjecture is one of the most important problems in modular representation theory of finite groups. The conjecture states that a block of a finite group with abelian defect group would be derived equivalent to its Brauer correspondent block. In this project, I calculated some examples for the conjecture and try to generalize such results. I also had some results for trivial source modules, which are important for constructing stable equivalences, calculating modules of images of simple modules under the stable equivalences.