Cohomology of finite groups from the view point of representation theory

我们用表示论的方法研究了有限群和有限维代数的上同调理论。我们考虑了由Hochschild上同调定义的模簇和外部代数或分次Hopf代数上的模的秩簇。特别地，我们得到了关于模的张量积的一些结果。另一方面，我们研究了双Burnside代数在有限群的mod-p上同调代数上的作用，得到了一些关于合成因子的结果。

We studied the cohomology theory of finite groups and finite dimensional algebras using methods of representation theory. We considered the varieties of modules defined by Hochschild cohomology and the rank varieties of modules over exterior algebras or graded Hopf algebras. In particular, we obtained some results on tensor products of modules. On the other hand, we studied the action of double Burnside algebra on the mod-p cohomology algebra of a finite group and obtained some results on composition factors.