On a derived equivalence classification for blocks of finite groups

Broue的交换亏群猜想是有限群模表示理论中最重要的问题之一。该猜想指出具有交换亏群的有限群的一个块与其对应的Brauer块等价。在这个项目中，我计算了一些猜想的例子，并试图推广这些结果。我也得到了一些关于平凡源模的结果，这些结果对于构造稳定等价、在稳定等价下计算简单模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.