Algebra Seminar

One of the main problems in modular representation theory is to understand the connections between local and global representations of a finite group G. In other words, one frequently tries to understand the representations of G over a field k of characteristic p>0 by studying representations for the normalizers of nontrivial p-subgroups, known as local subgroups. The stable category kG-Mod is defined by factoring out the projectives in the category kG-Mod of all left kG-modules. This talk will discuss a way of using the local structure of G to construct a category L(G,k) that is equivalent to kG-Mod. It is then easy to identify an appropriate subcategory of L(G,k) that is equivalent to the subcategory kG-mod of finitely generated modules in kG-Mod.